Investigation of No-load and on-load performance of a ...

Investigation of No-load and on-load performance of a

model three-phase transformer core operating under

sinusoidal and PWM voltage excitation

By

Nabiel Mahmoud Dgali

Thesis submitted in fulfilment of the requirement for the degree

of Doctor of Philosophy

Wolfson Centre for Magnetics

School of Engineering, Cardiff University

Investigation of No-load and on-load performance of a model three-phase transformer

core operating under sinusoidal and PWM voltage excitation

i

Declaration

This work has not been submitted in substance for any other degree and is not

concurrently submitted in candidature for any degree.

Signed: Nabiel Mahmoud Dgali (candidate) Date

STATEMENT 1

This thesis is being submitted in partial fulfilment of the requirements for PhD

degree.


STATEMENT 2

This thesis is the result of my own work and investigation, except where otherwise

stated. Other sources are acknowledged by explicit references.


STATEMENT 3

I hereby give consent for my thesis, if accepted, to be available for photocopying and

for inter-library loan, and for the title and summary to be made available to outside

organisation.




ii

Acknowledgments

The work was carried out at the Wolfson Centre for Magnetic Technology,

Department of Electrical and Electronic Engineering, Cardiff University. And thanks

to Dr Fatih Anayi for readily allowing me the use of the facilities of the Department.

I wish to express my profound gratitude to my supervisor, Dr Fatih Anayi for his

guidance, assistance, encouragement and his vast knowledge and skills in many

areas, and his advice during the period of my research.

Besides my supervisor, I would like to express my special thanks to Dr Yevgen

Melikhov for his advice during the course of my study. And thank the other members

of Wolfson Centre, Dr Philip Anderson and Dr Turgut Meydan for their advice and

comments at all levels of my research. I would also like to thank Mrs Christine Lee,

Mrs Aderyn Reid, Ms Jeanette C Whyte, in research office and Mr Denley Slade and

David Billings in electronic workshop and Mr Steve Mead, Mr Malcolm Seaborne,

Mr Andrew Rankmore and Mr Mal lyall in mechanical workshop for taking time out

from their busy schedule to help and support my project during my study in Cardiff

University.

Finally, my greatest thanks go to my family, for their unconditional love, support and

encouragement in whole my life.



iii

Summary

The iron losses in transformer laminated cores is higher than the nominal losses of

the material itself by a factor known as the building factor. Reduction of the building

factor of a transformer core is as important as the improvement of the basic

properties of the material. In this investigation grain oriented 100 kVA three-phase

distribution transformer core was investigated in order to obtain detailed study of

losses. The core used in this study has overall dimensions of 540 mm in length and

520 mm in width. The core was built of 120 laminations as single joint three

lamination per stacking layer with length of overlap shift of 3 mm and density of

7650 kg/m3

. The core has the [011] [100] texture which is known as the Goss texture

or Cube-on edge texture. This study considers four aspects of losses and localised

magnetostriction on transformer core.

Firstly, the power loss under sinusoidal and PWM excitation in the three-phase

transformer core which was made up of 3% silicon Highly Grain-Oriented material

(HGO) was measured. Also, the power loss of Epstein strips at various flux density

and frequencies was measured. In addition, localised and overall flux density

distributions in depth under sinusoidal and PWM excitation conditions in the

transformer core at core flux densities of 0.4T, 0.6T and 1.0T under load and no-load

conditions were measured.

Secondly, the effect of the clamping pressure on overall and localised power loss was

determined under sinusoidal and PWM voltage excitations. The results showed that

the loss under PWM voltage excitation increased by 10-30% as the flux density is

increased. Further, the shape of the excitation voltage as well as the switching

frequency spectrum and modulation index values also played a major role in the

power loss.

Thirdly, the influence of localised magnetostriction on the three-phase transformer

core was investigated under sinusoidal and PWM voltage excitations by measuring

the mechanical strain distribution in the transformer core under different peak flux

densities. The investigation showed that increasing the peak flux density from 0.4T

to 1.0T increased localised magnetostriction where the largest localised

magnetostriction was obtained at the T-joints.



iv

Finally, using MATLAB environment comparisons have also been made between the

results obtained from sinusoidal and PWM inverter. These results showed that the

localised and overall power loss increased considerably under PWM voltage

excitation. Comparisons have also been made between practical core and the

simulated model magnetic core results. These results showed that lower power losses

occurred under simulated results because the model core had zero flux leakage.



v

List of Abbreviation and Nomenclatures

Abbreviations

B Flux density

CGO Conventional grain oriented

DAQ Data acquisition

H Magnetic field

HGO High permeability grain oriented

L Length

LDR Laser scribed domain refined

M Magnetization

PWM Pulse width modulation

RMS Root mean square

RD Rolling direction

SST Single strip/ sheet tester

TD Transvers direction

THD Total harmonic distortion

V Voltage

Subscripts

Variables in the RD

Variables in the TD

Symbols

ɸ Flux density

Peak flux density

µ Permeabiliy



vi

Hysteresis loss constant

Sample length

Change in length

Flux density of the material

Permeability of free space

M Magnetisation

Saturation magnetisation

Remnant magnetisation

Number of step laps

, Number of turns of the primary and secondary windings

Average power loss per cycle

Loss due to eddy currents in electrical steel laminations

Loss due to hysteresis in electrical steel laminations

Excess loss in electrical steel lamination

Specific power loss

Specific power loss component along RD

Specific power loss component along TD

Overall power loss

Shunt resistance

Strain gauge resistance

Time

Secondary phase voltage in 3-phase, 3-limb, transformer core

Root mean square value of the secondary voltage



vii

Overall voltage

Fundamental voltage harmonic components

Average value of the secondary voltage

Amplitude of Sinusoidal signal

Amplitude of carrier voltage signal

σ Conductivity of magnetic core

Thickness of the lamination sheet

Modulation index

Frequency modulation ratio

Clamping pressure

Saturated magnetostriction

Young’s module in the rolling and transvers direction

χ Magnetic susceptibility

Magnetostriction

Magnetostriction in the RD

Magnetostriction in the TD

Strain



viii

Table of contents

Declaration…………………………………………………………………………………………………. .ii

Acknowledgments ........................................................................................................ ii

Summary ..................................................................................................................... iii

List of Abbreviation and Nomenclatures ..................................................................... v

Table of contents ....................................................................................................... xvi

List of figures .......................................................................................................... xviii

List of tables ............................................................................................................. xxv

1. Introduction .......................................................................................................... 1

Parameters of magnetic field .................................................................. 1 1.1.1

Ferromagnetic and non-ferromagnetic materials ................................... 2 1.1.2

Short survey of ferromagnetism ............................................................. 3 1.1.3

Basic properties ...................................................................................... 4 1.1.4

1.2 Transformer core materials ........................................................................... 5

Development of silicon-iron alloys ........................................................ 6 1.2.1

Coatings ................................................................................................. 8 1.2.2

Stress sensitivity ..................................................................................... 8 1.2.3

Mechanical stress ................................................................................... 9 1.2.4

1.3 Transformer core design and coating. ........................................................... 9

Transformer cores corner joints ........................................................... 13 1.3.1

Cross-section of transformer cores....................................................... 15 1.3.2

Flux density harmonics ........................................................................ 171.3.3



ix

Core performance ................................................................................. 17 1.3.4

1.4 Power loss in silicon-iron transformer cores ............................................... 17

Power loss due to core materials .......................................................... 18 1.4.1

Power loss due to construction of the cores ......................................... 18 1.4.2

Magnetostriction in ferromagnetic material ......................................... 18 1.4.3

Previous related work ........................................................................... 21 1.4.4

Aims of the Investigation ..................................................................... 22 1.4.5

CHAPTER 2 .............................................................................................................. 24

2. Type of the transformer core materials .............................................................. 24

Grain oriented steel .............................................................................. 24 2.1.1

Non- oriented steel ............................................................................... 24 2.1.2

Laser scribed domain refined (LDR) ................................................... 25 2.1.3

2.2 Transformer theory and performance .......................................................... 26

Overall flux density measurement under sinusoidal excitation ........... 28 2.2.1

Overall flux density measurement under PWM voltage excitation ..... 30 2.2.2

Fundamental theory of localised power loss measurement in 2.2.3

transformer cores ................................................................................................ 31

Total iron losses using loss separation criteria ..................................... 32 2.2.4

2.3 Hysteresis losses .......................................................................................... 33

Eddy current losses .............................................................................. 35 2.3.1

Anomalous loss .................................................................................... 36 2.3.2

Theory of estimates of iron loss components using loss separation 2.3.3

criteria 38

Flux density distribution ...................................................................... 39 2.3.4

2.4 Overall flux density distribution under sinusoidal voltage excitation ......... 40



x

Overall flux density distribution under PWM voltage excitation ........ 43 2.4.1

Field and flux measurement method .................................................... 45 2.4.2

Magnetic field measurement ................................................................ 45 2.4.3

H -coil construction and calibration ..................................................... 45 2.4.4

CHAPTER 3 .............................................................................................................. 48

3. Pulse width modulation (PWM)......................................................................... 48

Modulation index ................................................................................. 49 3.1.1

Switching frequency............................................................................. 49 3.1.2

Voltage source inverter ........................................................................ 50 3.1.3

Current source of PWM inverter .......................................................... 51 3.1.4

3.2 Magnetizing current variation under PWM voltage excitation ................... 52

Magnetizing current variation under sinusoidal voltage excitation ..... 57 3.2.1

Comparison of the results .................................................................... 62 3.2.2

Effect of switching frequency on overall flux density ......................... 64 3.2.3

3.3 Overall power losses under sinusoidal waveform ....................................... 67

Setup of the measurement of overall power loss ................................. 67 3.3.1

Effect of clamping pressure ................................................................. 74 3.3.2

Analysis and discussion ....................................................................... 75 3.3.3

Order harmonic content with a change in peak flux density ................ 75 3.3.4

CHAPTER 4 .............................................................................................................. 78

4. Experimental apparatus and measuring technique ............................................. 78

Core geometry ...................................................................................... 78 4.1.1

Type of joints ....................................................................................... 80 4.1.2

Support and clamping .......................................................................... 804.1.3



xi

4.2 Localised flux density calculation ............................................................... 83

Localised flux density measurement .................................................... 84 4.2.1

Construction and positioning of search coils ....................................... 85 4.2.2

Calibration and testing of search coils ................................................. 85 4.2.3

Measurement preparation ..................................................................... 86 4.2.1

4.3 Measurement results of localised power loss .............................................. 88

Comparison of the results .................................................................. 107 4.3.1

Localised power loss obtained in the outer limb of the model three-4.3.2

phase transformer core with various peak flux densities ................................. 108

Localised power loss obtained in the middle limb of the model three-4.3.3

phase transformer with various peak flux densities ......................................... 112

Comparison between localised power loss obtained in the middle of the 4.3.4

outer and central limbs of the model three-phase transformer core with various

peak flux densities ............................................................................................ 115

Localised power loss obtained in the limb corner joints of the model 4.3.5

three-phase transformer core with various peak flux densities ........................ 116

Localised power loss obtained in the yoke corner joints of the model 4.3.6

three-phase transformer core with various peak flux densities ........................ 118

Comparison between localised power loss obtained in the limb and 4.3.7

yoke corner joints of the model three-phase transformer core with various peak

flux densities .................................................................................................... 121

Localised power loss obtained in the yoke- 045 joints with various peak 4.3.8

flux densities .................................................................................................... 122

Localised power loss obtained in the limb T joints with various peak 4.3.9

flux densities .................................................................................................... 126

Comparison between power loss obtained in the limb and yoke T joints 4.3.10

with various peak flux densities ....................................................................... 129



xii

Influence of modulation index and switching frequency on total power 4.3.11

loss in three-phase transformer core. ............................................................... 131

Analysis and discussion ..................................................................... 133 4.3.12

CHAPTER 5 ............................................................................................................ 134

5. Introduction ...................................................................................................... 134

Magnetostriction ............................................................................. 134 5.1.1

Domain wall and spontaneous magnetostriction................................ 135 5.1.2

Saturation magnetostriction ............................................................... 136 5.1.3

Transformer noise .............................................................................. 137 5.1.4

5.2 Winding noise ............................................................................................ 137

Fans and pump noise .......................................................................... 137 5.2.1

Magnetic core vibration ..................................................................... 137 5.2.2

Core construction and design ............................................................. 137 5.2.3

Magnetostriction characteristic under applied field ........................... 138 5.2.4

5.3 Method used to measure magnetostriction ................................................ 139

Piezoelectric displacement transducer ............................................... 139 5.3.1

Linear variable differential transformer ............................................. 140 5.3.2

Capacitive displacement sensors ........................................................ 141 5.3.3

Laser Doppler techniques ................................................................... 141 5.3.4

5.4 Pro foils strain gauges ............................................................................... 142

Three-wire strain gauge rosettes pre-wired ........................................ 143 5.4.1

Strain data logger ............................................................................... 144 5.4.2

Strain gauge sample preparation ........................................................ 146 5.4.3

Magnetostriction calculation .............................................................. 152 5.4.4

5.5 Investigation of localised magnetostriction within transformer core ........ 153



xiii

Stress .................................................................................................. 158 5.5.1

Stress calculation ................................................................................ 158 5.5.2

Noise and vibration phenomena in transformer core ......................... 159 5.5.3

Influence of magnetic flux density on transformer core 5.5.4

magnetostriction and vibration ......................................................................... 160

5.6 Core vibration and sound level measurement (SPL) ................................. 160

Analysis and Discussion .................................................................... 161 5.6.1

Localised magnetostriction under PWM and sinusoidal voltage 5.6.2

excitation in three-phase transformer core in horizontal position .................... 161

Localised magnetostriction under PWM and sinusoidal voltage 5.6.3

excitation in three-phase transformer core in vertical position ........................ 164

CHAPTER 6 ............................................................................................................ 166

6. Measurement with the Epstein Frame .............................................................. 166

Single Strip Tester measurement ....................................................... 168 6.1.1

Power loss in electrical steel based on two-term formula .................. 172 6.1.2

Power loss in electrical steel based on three-term formula ................ 173 6.1.3

6.2 Loss separation using extrapolation method based on the two-term

formulation ........................................................................................................... 173

Loss separation using extrapolation method based on the three-term 6.2.1

formulation ....................................................................................................... 174

Experimental results under PWM voltage excitation at 0.4 T ........... 175 6.2.2

Experimental results under PWM voltage excitation at 1.0 T ........... 178 6.2.3

Experimental results under sinusoidal voltage excitation at 0.4T...... 180 6.2.4

6.3 Experimental results under sinusoidal voltage excitation at 1.0 T ............ 182

Comparison of the results .................................................................. 186 6.3.1

7. CHAPTER 7 .................................................................................................... 187



xiv

MATLAB block diagram contents..................................................... 187 7.1.1

Simulation under sinusoidal voltage excitation ................................. 188 7.1.2

Simulation under PWM voltage excitation ........................................ 190 7.1.3

Total harmonic distortion under sinusoidal voltage excitation .......... 192 7.1.4

7.2 Total Harmonic Distortion, THD under PWM Voltage Excitation .......... 194

Total harmonic contents with a change in switching frequency ........ 197 7.2.1

Harmonic analysis .............................................................................. 199 7.2.2

Power loss analysis ............................................................................ 200 7.2.3

Specific losses with a change in PWM modulation index ................. 202 7.2.4

Total losses with a change in PWM switching frequency ................. 204 7.2.5

Summary ............................................................................................ 206 7.2.6

CHAPTER 8 ............................................................................................................ 207

8. Conclusion and suggestion for future work ..................................................... 207

Conclusion ......................................................................................... 207 8.1.1

Suggestion for future work................................................................. 209 8.1.2

1



xvi

List of figures

Fig. ‎1-1 Domain pattern under magnetizing process .............................................................................. 3

Fig. 1-2 Hysteretic magnetisation of grain oriented electrical steel [4].................................................. 5

Fig. ‎1-3 Schematic diagram of square orientation .................................................................................. 7

Fig. 1-4 Effect of stress on domain pattern ............................................................................................ 8

Fig. ‎1-5 Different cores structures ........................................................................................................ 10

Fig. ‎1-6 Forms of cores built from wound strips. (a) Single-phase core type. (b) Single-phase shell

type. (c) Three-phase core type ............................................................................................................ 11

Fig. ‎1-7 (a,b) Three phase transformer core with involute legs and Symmetrical magnetic system .... 12

Fig. ‎1-8 Square joint ............................................................................................................................. 13

Fig. ‎1-9 350/550 Miter joint ................................................................................................................. 13

Fig. ‎1-10 Mitred corners....................................................................................................................... 14

Fig. ‎1-11 Step-lap joint ........................................................................................................................ 14

Fig. ‎1-12 450 Mitre joints .................................................................................................................... 15

Fig. ‎1-13 Cross sectional area of transformer core – limbs .................................................................. 16

Fig. ‎1-14 Magnetic domain wall in ferromagnetic materials ............................................................... 19

Fig. ‎1-15 Effect of magnetostriction (a) zero field (b) applied field .................................................... 20

Fig. ‎2-1 Ideal single-phase transformer core [3] .................................................................................. 26

Fig. ‎2-2 Positions of the localised search coils ..................................................................................... 39

Fig. ‎2-3 Position of the reference search coils ..................................................................................... 41

Fig. ‎2-4 Variation of the induced voltage against time under sinusoidal waveform in the transformer

limb at 0.4T .......................................................................................................................................... 42

Fig. ‎2-5 Variation of the induced voltage against time under sinusoidal waveform in the transformer

yoke at 0.4T .......................................................................................................................................... 42



xvii

Fig. ‎2-6 variation of the overall flux density against time (ms) before the integrator circuit ............... 43

Fig. ‎2-7 variation of the overall flux density against time (ms) after integrator circuit ....................... 43

Fig. ‎2-8 Schematic diagram of solenoid system .................................................................................. 46

Fig. ‎2-9 Voltage vs magnetic field with assign value of flux density .................................................. 47

Fig. ‎3-1 . PWM waveform generators [3] ........................................................................................... 48

Fig. ‎3-2 Three-phase PWM inverter voltage configuration circuit [4] ................................................. 50

Fig. ‎3-3 Schematic diagram of controlled current S1, S2 Switch. L: Inductance R: Resistor [1] ....... 51

Fig. ‎3-4 Block diagram for measuring magnetising current ................................................................. 52

Fig. ‎3-5 Variation of magnetizing current at 0.3T in the outer limb with assigned values of switching

frequency .............................................................................................................................................. 53

Fig. ‎3-6 Variation of magnetizing current at 0.3T in the middle limb with assigned values of switching

frequency .............................................................................................................................................. 53

Fig. ‎3-7 Variation of magnetizing current at 0.4T in the outer limb with assigned values of switching

frequency .............................................................................................................................................. 54

Fig. ‎3-8 Variation of magnetizing current at 0.4T in the central limb with assigned values of switching

frequency .............................................................................................................................................. 54

Fig. ‎3-9 Variation of magnetising current at 0.7T in the middle limb with assigned values of switching

frequency .............................................................................................................................................. 55

Fig. 3-10 Variation of magnetising current at 0.7T in the outer limb with assigned values of switching

frequency .............................................................................................................................................. 56

Fig. ‎3-11 Variation of magnetising current under three-phase varaic under no-load condition at 0.3T 59

Fig. ‎3-12 Variation of magnetising current under three-phase varaic under load condition at 0.3T .... 59

Fig. ‎3-13 Variation of magnetising current under sinusoidal voltage excitation under no-load

Condition at 0.4T ................................................................................................................................. 60

Fig. ‎3-14 Variation of magnetising current under sinusoidal voltage excitation under Load Condition

at 0.4T .................................................................................................................................................. 60



xviii


Condition at 0.7T ................................................................................................................................. 61

Fig. ‎3-16 Variation of magnetising current under sinusoidal voltage excitation under load Condition at

0.7T ...................................................................................................................................................... 61

Fig. ‎3-17 Overall induced voltage under PWM voltage excitation (no-load conditions) with switching

frequency varied from 2 to 3 kHz at different peak flux density (T).................................................... 65

Fig. ‎3-18 Overall induced voltage under PWM voltage excitation (load conditions) with switching

frequency varied from 2 to 3 kHz at different peak flux density (T).................................................... 65


frequency varied between 8, 12, 16 kHz at different peak flux density (T) ......................................... 66


frequency varied between 12, 16 kHz at different peak flux density (T) ............................................. 66

Fig. ‎3-21 Overall power loss measurement system .............................................................................. 68

Fig. ‎3-22 Overall power loss at clamping pressure of 0 N/ 2 under no-load condition at different flux

densities ................................................................................................................................................ 69

Fig. ‎3-23 Overall power loss at clamping pressure of 8 N/ 2 under no-load condition at different flux

densities ................................................................................................................................................ 69

Fig. ‎3-24 Overall power loss at clamping pressure of 15 N/ 2 under no-load condition at different

flux densities ........................................................................................................................................ 70

Fig. ‎3-25 Overall power loss at clamping pressure of 27 N/m2 under no-load condition at different flux

densities ................................................................................................................................................ 70

Fig. ‎3-26 Overall power loss at clamping pressure of 0 N/m2 under load condition at different flux

densities ................................................................................................................................................ 72

Fig. ‎3-27 Overall power loss at clamping pressure of 8 N/m2 under Load Condition at different flux

densities ................................................................................................................................................ 72

Fig. ‎3-28 Overall power loss at clamping pressure of 15 N/ 2 under load condition at different flux

densities ................................................................................................................................................ 73



xix

Fig. ‎3-29 Overall power loss at clamping pressure of 27 N/m2 under load condition at different flux

densities ................................................................................................................................................ 73

Fig. ‎4-1 (a) Dimension of the middle limb. (b) Dimensions of the outer limb (c) Dimensions of the

yoke ...................................................................................................................................................... 79

Fig. ‎4-2 Three-phase transformer core ................................................................................................. 80

Fig. ‎4-3 Photograph of magnetising and associated measurement system ........................................... 82

Fig. ‎4-4 Block diagram of virtual instrument for calculating magnetic flux density ........................... 87

Fig. ‎4-5 Locations of localised search coils in the outer limb .............................................................. 91

Fig. ‎4-6 Locations of the search coils in the outer limb corner joint, rolling (R) and transvers

Directions (T) ....................................................................................................................................... 94

Fig. ‎4-7 Locations of the search coils in the outer yoke corner joint, rolling (RD) and transfer

directions (TD) ..................................................................................................................................... 97

Fig. ‎4-8 Locations of the search coils in the middle limb .................................................................. 100

Fig. ‎4-9 Locations and direction of the search coils in the T-joint ..................................................... 103

Fig. ‎4-10 Locations and directions of the search coils in the T-joint R and T directions ................... 106

Fig. ‎4-11 Comparison of localised power loss under sinusoidal and PWM voltage excitations (No-load

condition) at the center of the outer limb at various peak flux densities (T), 50 Hz. ......................... 111

Fig. ‎4-12 Comparison of localised power loss under sinusoidal and PWM voltage excitations (Load

condition) at the center of the outer limb at various peak flux densities (T), 50 Hz. ......................... 111

Fig. ‎4-13 Comparison of localised power loss under sinusoidal and PWM voltage excitation (No-load

condition) central limb at various peak flux densities (T), 50 Hz ...................................................... 114

Fig. ‎4-14 Comparison of localised power loss under sinusoidal and PWM voltage excitation (Load

condition) central limb at various peak flux densities (T), 50 Hz ...................................................... 114


condition) at limb corner joints at various peak flux densities (T), 50 Hz. ........................................ 117



xx


condition) at limb corner joints at various peak flux densities (T), 50 Hz. ........................................ 118

Fig. ‎4-17 Comparison of localised power loss under sinusoidal and PWM voltage excitation (no-load

condition) at yoke corner joints at various peak flux densities (T), 50 Hz. ........................................ 120


condition) at various peak flux densities (T), 50 Hz. ......................................................................... 121

Fig. ‎4-19 Comparison of localised distribution of power loss under sinusoidal and PWM voltage

excitation (No-load condition) at various peak flux densities (T), 50 Hz .......................................... 124


condition) at various peak flux densities (T), 50 Hz .......................................................................... 124


condition) at limb T-joints at various peak flux densities (T), 50 Hz. ................................................ 128


condition) at limb T-joints at various peak flux densities (T), 50 Hz. ................................................ 128

Fig. ‎4-23 Total power loss under PWM voltage excitation with assigned value of modulation index at

3 kHz ............................................................................................................................................. 131


2 kHz ............................................................................................................................................. 132


1 kHz ............................................................................................................................................. 132

Fig. ‎5-1 Mechanism of magnetostriction ........................................................................................... 135

Fig. 5-2 Domain walls rotate to the applied field ............................................................................... 138

Fig. 5-3 Magnetostriction measurement systems using piezoelectric transduces technique .............. 139

Fig. ‎5-4 Schematic diagram of LVDT ................................................................................................ 140

Fig. ‎5-5 Block diagram of a laser doppler velocimeter ...................................................................... 141

Fig. 5-6 Pro Foil strain gauge used to Measure magenetostriction .................................................... 142



xxi

Fig. 5-7 Shows 3-Wire Strain Gauge Rosettes Pre-wired .................................................................. 143

Fig. ‎5-8 Strain gauges measurement system ...................................................................................... 145

Fig. 5-9 Strain gauges measurement connection ................................................................................ 147

Fig. 5-10 Positions of pro foil strain gauges selected position ........................................................... 148

Fig. ‎5-11 Positions of three-wire strain gauges Roesttes pre-wired ................................................... 149

Fig. 5-12 Position of the robber placed around Pro-foil strain gauges ............................................... 151

Fig. ‎5-13 Position of the robber placed around three- wire strain gauges Rosettes pre-wired ........... 151

Fig. 5-14 Three-phase magnetic flux density waveforms [20] ........................................................... 159

Fig. ‎6-1 Epstein frame and double overlapped joints ......................................................................... 166

Fig. 6-2 Schematic diagram of computer-controlled Single Strip Tester (SST)................................. 169

Fig. ‎6-3 Measurement system of single strip tester ............................................................................ 170

Fig. ‎6-4 Single strip tester .................................................................................................................. 171

Fig. ‎6-5 Specific power loss per cycle versus square root of frequency at 0.4T under PWM voltage

excitation ............................................................................................................................................ 176

Fig. ‎6-6 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 0.4T under PWM voltage

excitation ............................................................................................................................................ 177

Fig. 6-7 Specific power loss per cycle versus root of frequency at 1T under PWM voltage excitation

............................................................................................................................................................ 179

Fig. ‎6-8 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 1T under PWM voltage

excitation ............................................................................................................................................ 179

Fig. 6-9 Specific power loss per cycle versus square root of frequency at 0.4T under sinusoidal voltage

excitation ............................................................................................................................................ 181

Fig. 6-10 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 0.4T under sinusoidal

voltage excitation ............................................................................................................................... 182



xxii

Fig. 6-11 Specific power loss per cycle versus square root of frequency at 1T under sinusoidal voltage

excitation ............................................................................................................................................ 184

Fig. 6-12 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 1T under sinusoidal

voltage excitation ............................................................................................................................... 185

Fig. 7-1 Sinusoidal voltage excitation circuit under load condition ................................................... 188

Fig. ‎7-2 Sinusoidal voltage excitation circuit under no-load condition .............................................. 189

Fig. ‎7-3 PWM voltage excitation circuit under load condition .......................................................... 190

Fig. ‎7-4 PWM voltage excitation circuit under no-load condition ..................................................... 191

Fig. ‎7-5 Harmonic order content of primary current for sinusoidal supply voltage under no-load

condition with different peak flux density (T) ................................................................................... 192

Fig. ‎7-6 Harmonic order content of primary current for sinusoidal supply voltage under on-load


Fig. ‎7-7 Harmonic order content of primary voltage for sinusoidal supply voltage under no-load


Fig. ‎7-8 Harmonic order content of primary voltage for sinusoidal supply voltage under on-load


Fig. ‎7-9 Harmonic order content of primary current for PWM supply voltage under on-load condition

with different peak flux density (T) ................................................................................................... 195

Fig. ‎7-10 Harmonic order content of primary current for PWM supply voltage under no-load


Fig. ‎7-11 Harmonic order content of secondary voltage for PWM supply voltage under on-load


Fig. ‎7-12 Harmonic order content of secondary voltage for PWM supply voltage under no-load


Fig. ‎7-13 Harmonic order contents of primary current for PWM supply voltage under on-load

condition at switching frequency 3 kHz ............................................................................................. 197



xxiii

Fig. ‎7-14 Harmonic order contents of secondary voltage for PWM supply voltage under on-load






Fig. ‎7-19 Overall power loss of three-phase transformer core supplied by sinusoidal and PWM

waveforms with change in the peak flux density (T) at 50 Hz at Mi= 0.5 and Fs= 3kHz .................. 201

Fig. ‎7-20 Total power losses of the three-phase transformer core supplied by PWM waveform with

change in the modulation index at 3kHz switching frequency. .......................................................... 202


change in the modulation index at 2kHz switching frequency ........................................................... 203


change in the modulation index at 1 kHz switching frequency .......................................................... 203

Fig. ‎7-23 Total power loss of the three-phase transformer core with change in switching frequency at

constant modulation index of 0.5 ....................................................................................................... 204







xxv

List of tables

Table ‎2-1 Overall voltage calculation of desired peak flux density under sinusoidal excitation ......... 29

Table ‎2-2 overall voltage calculation of desired peak flux density under PWM excitation ................. 31

Table ‎2-3 saturation value of some material [3,5,6] ............................................................................. 34

Table ‎2-4 Induced B ( ) in the reference search coil ...................................................................... 41

Table ‎2-5 Variation of fundamental components of overall flux density in the limbs and yokes ........ 44

Table ‎2-6 Output voltage and current from solenoid core .................................................................... 47

Table ‎3-1 Current required for desired flux density under no-load condition ...................................... 58

Table ‎3-2 Current Required for Desired Flux Density under Load Condition ..................................... 58

Table 3-3 Overall Power under No-load condition .............................................................................. 68

Table 3-4 Overall power loss under load condition ............................................................................. 71

Table 6-1 Power loss per cycle under PWM voltage excitation at 0.4 T at different magnetising

frequencies ......................................................................................................................................... 175

Table 6-2 Measured and total power loss component of Epstein size lamination under PWM voltage

excitation at 0.4T with different magnetising frequencies ................................................................. 177

Table 6-3 Power loss per cycle under PWM voltage excitation at 1.0 T at different magnetising

frequencies ......................................................................................................................................... 178

Table 6-4 Measured and total power loss component of Epstein size lamination under PWM voltage

excitation at 1.0 T with different magnetising frequencies ................................................................ 178

Table 6-5 Power loss per cycle under sinusoidal voltage excitation at 0.4 T at different magnetising

frequencies ......................................................................................................................................... 180

Table 6-6 Specific and total power loss of an Epstein size lamination under sinusoidal voltage

excitation at 0.4T and different magnetising frequencies ................................................................... 180

Table 6-7 power loss per cycle at 1.0 T at different magnetising frequencies ................................... 183

Table 6-8 Specific and total power loss of an Epstein size lamination under sinusoidal voltage

excitation at 1.0 T at different magnetising frequencies .................................................................... 183



1

CHAPTER 1

1. Introduction

Electrical steels are the most considered material in terms, of studying magnetic

power loss performance under a particular peak flux density and magnetising

frequency of 50 and 60 Hz. Magnetic permeability and magnetostriction of electrical

steel is also considered as important properties. In this chapter fundamental terms in

magnetic materials, magnetising process, magnetic power loss mechanisms in

electrical steel, developing of transformer design and related issues have been

discussed.

Parameters of magnetic field 1.1.1

The parameters of a magnetic field are the magnetic field strength, H, magnetic flux

density, B, and magnetisation, M.

The magnetic field strength is measured in amperes per meter (

). Magnetic

field is the force which produces, or is associated with the magnetic induction at that

point [1]. The magnetic flux density (B) is measured in Weber per meter square (

)

or Tesla is a vector quantity that determines the induced . The relationship

between and B in air is written as:

B = H … (1.1)

Where is the permeability of free space ( -7

H/m)

The magnetization, M, is measured in Weber per square meter (W/ ) or Tesla (T)

the three quantities relationships are,

B = O ( + M) … (1.2)

The magnetization (M) at any point in a magnetic field is a vector lying in the same

direction as H at that point is directly proportional to the magnetic intensity within

the material thus,



2

M= H … (1.3)

Where is the magnetic susceptibility of the material and is in turn a function of H.

Substituting Eq. (1.3) in Eq. (1.2) and putting 1 + = µr where µr is the relative

permeability, we get:

B = µo (H + M) = µo H + µo M

B = µo H + µo H = µo H (1+ ) = µo µr H … (1.4)

µr in Electromagnetic units for free space is equal to 1. Magnetic circuit is usually

solved in term of (B) and H, where M is seldom used, but when necessary, its value

can be found from equation (1.3).

Ferromagnetic and non-ferromagnetic materials 1.1.2

Magnetic properties of all materials are divided into three types: diamagnetic,

paramagnetic and ferromagnetic.

Diamagnetic materials are: copper, gold, silver and bismuth which have relative

permeability (µr) slightly less than unity (for bismuth it is 0.99983). Their magnetic

response is in opposition to the applied magnetic field.

Paramagnetic materials are: aluminium, platinum and manganese which have relative

permeability (µr) slightly greater than unity (for platinum it is 1.00036). These

materials exhibit weaker magnetisation (M) whose direction is aligned towards the

magnetic field.

Ferromagnetic materials are: iron, cobalt and nickel those which have high values of

relative permeability, up to 104 or even 10

6,

In electrical engineering it is suffice to class all materials simply as ferromagnetic or

non-ferromagnetic. The former includes materials of relative permeability many

times greater than unity while the latter has relative permeability practically equal to

unity. (µr) is used to classify the magnetic materials.



3

Short survey of ferromagnetism 1.1.3

Ferromagnetic materials are composed of many small regions or domains, each

displaying a net magnetization [2], even under no external magnetic field magnetic

domains line up. The magnetization vector of each domain point in a direction which

depends on the elastic stresses present inside a given material and its crystal

structure. As shown in Fig. 1-1 (A) under ordinary conditions the vectors of the

individual domains re-directed at random and cancel their magnetic moment, thus

leaving the samples as a whole with no resultant magnetization. When an external

magnetic field is applied as shown in Fig. 1-1 (B) the domains become re-arranged,

producing a net magnetization along the applied field. Continue to increase the

applied magnetic field the spontaneous (MS) rotate all domains in sample into one

direction so the sample reach the saturation point as shown in (C). Owing to this, the

resultant magnetic induction becomes many times greater than the applied magnetic

field ( by hundred or even hundred thousand times) [3].

Fig. ‎1-1 Domain pattern under magnetizing process



4

The most advantageous state for ferromagnetic materials is such that it is subdivided

into many domains with their magnetic moments anti-parallel to one another. Then

the total magnetostatics energy of the system will be a minimum.

Basic properties 1.1.4

The magnetic properties of ferromagnetic materials are conveniently represented by

drawing curves of B against H. As shown in these are magnetization curves and

hysteresis curves.

Ferromagnetic materials exhibit a hysteresis between the magnetic induction and the

applied magnetic intensity [4] the phenomenon of hysteresis is analogues to

mechanical inertia. This is due to the friction occurring in the domain wall. When

external magnetic field applied net magnetisation in the material is not zero. This

occurs by the movement of the domain wall to the direction of the applied filed point

1(red dots between point f and point b).

Increasing the applied field during the magnetisation domain walls rotate out of the

easy axes of magnetisation into the direction of the applied field and reach the

saturation value point (a). Since the domain is being moved from its original position

to new a position this leads to production of magneto – static energy. For a material

which has never been magnetized (virgin state), many cycles of magnetization may

be required before a closed loop is obtained, the one obtained for is referred to

as the major hysteresis loop, and the material is said to be cyclically magnetized.

When the applied magnetising field is removed, the magnetic induction always lags

behind the change in the applied H the magnetic induction is still near its saturation

value point (b) remnant flux density. In order to reduce B to zero, a negative field

called the coercive force must be applied point (c).



5

Fig. ‎1-2 Hysteretic magnetisation of grain oriented electrical steel [4]

1.2 Transformer core materials

There are essentially two main grades of electrical steels for use in power

transformer: grain-oriented steel and non - oriented steel.

Non-oriented steels offer magnetic properties in a primarily random pattern with

respect to the direction of rolling. An oriented material refers to the materials crystal

structure with magnetic properties substantially better in the direction of rolling [5].

Two different grades are supplied by the manufacture, non-oriented non-silicon steel

and non-oriented silicon steel, Both types of material can be supplied either fully

processed or semi-processed. Semi-processed with or without a stress-relief

annealing. Non-oriented electrical steels are made to final thickness of 0.35 mm, 0.50

mm or 0.65 mm. For special application, 1.0 mm thick laminations may be used.

Non-oriented Si-Fe steel contains a range of silicon from about 0.5% to 3.2%.

Adding silicon to the steel increase the resistivity and decrease the permeability of

the steel and result in lower eddy current losses but increase the hysteresis losses if

the amount of the steel exceeds 3.5%, the steel cannot be rolled in acceptable

direction.



6

Grain oriented 3% silicon steel used to build transformer cores and large rotating

machines because it has very low iron losses. Moreover, the losses of the best grain-

oriented steel are about 70% less than the best grades of non-oriented electrical steel.

In general, oriented electrical steels are more expensive than non-oriented steel but

offer substantially better magnetic properties. For example, under certain conditions,

the difference in the exciting currents for a favourable direction and an unfavourable

direction in grain-oriented steels may be more than 20 times greater than the

difference in case of the non-oriented steel [6].

Development of silicon-iron alloys 1.2.1

Early transformer cores were built using solid iron cores. In 1882 Hadfield observed

the adding silicon to high purity steel can improve the coercive force and

permeability which was accidentally produced [7].

Since 1903 silicon-iron alloys have been used in transformer cores and many

research works have been carried out to reduce the core losses, minimise the eddy

current and increase the permeability of the material. Silicon content of the steel is

3.2% by weight if the silicon is higher than 3.2% the steel become brittle and hard to

assemble. However, the losses are now are approximately one third of what they

were in 1910. In addition to improvement in power loss, there were great savings in

space.

In 1934 the greatest drop in core loss was achieved by Goss [8] with the invention of

((Grain-Oriented Silicon Steel)). This process including heat treatment and cold

rolling product. These treatments have been used to cultivation desired grain texture

with a direction of easy magnetization parallel to the rolling direction, the

magnetization should be in this direction, since in the transvers direction the loss is

about three times greater [9].

Other method were developed [10, 11] to control the crystallization by processing

silicon-iron sheet with certain purities, so that both rolling and transvers directions

have easy magnetization and low loss (Four Square or Cube orientation (010) [100]).

Fig. 1-3 progress in commercial production was also made [12, 13]. Various



7

impurities which were used to control the recrystallization texture are: oxygen,

sulphur, vanadium nitride and aluminium nitride [14].

Other method recently introduced is laser scribed domain refined (LDR) this method

reducing the width of magnetic domain by laser irradiation process, this process

reduce heat in the sheet.

Fig. ‎1-3 Schematic diagram of square orientation



8

Coatings 1.2.2

Transformer laminations are coated on either side with thin layer of insulating

coating [15] these coating helps to provide electrical insulation between the adjacent

laminations and also prevent corrosion. On the other hand, coating produce stress

and increase the core mass weight. Coatings can be made of inorganic material, a

mixture of inorganic and organic materials. The typical coating thickness various

between 2 m to 5 m.

Stress sensitivity 1.2.3

The magnetic properties of Goss-oriented steel are sensitive to stress. The effects of

compressive stress along the rolling direction have been investigated by several

authors [16] [17].

Corner and Mason [18] have shown that the increase in power loss is due to the

change of the ideal ((bar domain)) which becomes difficult to magnetize and needs

extra magnetization.

Fig. ‎1-4 Effect of stress on domain pattern

When stress is applied to the transformer core, some of the domain walls will be

slightly misaligned. However, this domain movement is the primary generator of

magnetostriction in the core. In commercial production this sensitivity of the steel to



9

compression has been overcome by using insulating coating which keeps the material

under tension.

Mechanical stress 1.2.4

In the transformer cores, stresses are present, and it is very difficult to eliminate

them. These stresses are presented due to:

(1) Waviness of the laminations

(2) Bending induced by the weight of the laminations

(3) Clamping force

(4) Temperature gradients due to non-uniform distribution of flux density

The effect of stress results in increasing power losses in transformer core [19]. In

general, compressive stresses are the main causes of increasing power losses.

1.3 Transformer core design and coating.

Laminated core

Transformer cores are always built of strip cut or punched from sheets of grain-

oriented steel. Different core structure are generally used as shown in Fig. 1-5 yokes

and limbs joints are always overlapped thus minimising the air gaps introduced into

the magnetic circuit. All these cores are assembled by stacking the laminations and

when completed, the core is clamped, and the upper yokes are removed. Then pre-

wound coils slipped into place and the top yoke are built again in its previous place.

The core is held together to avoid vibration and noise [6].



10

Fig. ‎1-5 Different cores structures



11

Wound core

In order to direct the flux to flow in one direction, wound core was introduced. These

types of core consist of spirals of silicon-iron strip wound by a machine. Then the

core is annealed to relieve stress induced by the bending of the sheet. This type of

cores can be used for single and three phase system, wound core build as core-type

and shell type Fig. 1-6 shows types of cores.

Fig. ‎1-6 Forms of cores built from wound strips. (a) Single-phase core type. (b) Single-phase

shell type. (c) Three-phase core type



12

Involute core

The first system had three limbs arranged uniformly in three plants along the

circumference of the yoke. The limbs are constructed in an involute curve forming a

thick-walled tube. Finally, core is formed by using triangular yokes at the top and

bottom. These cores are stress-relief annealed and are held together by means of

screws through the limbs as shown in Fig. 1-7. Experiment has been carried out on

involute core, it was found that the instantaneous fluxes in the limbs differ 0120 , and

the flux in the yoke is less than the maximum flux in the limb by a factor of √ .

Fig. ‎1-7 (a,b) Three phase transformer core with involute legs and Symmetrical magnetic system



13

Transformer cores corner joints 1.3.1

Transformer core built up using various types of joints [20], [21]. Fig. 1-8 to Fig. 1-

12 show transformer core joints. These joints link the limbs and the yokes.

Nevertheless, as transformer joints introduce air gapes, hence flux concentration,

cross fluxes, normal fluxes and rotational fluxes occur. The combination of these

effects increases the undesirable power loss [22].

Stacking singles layers ensures minimum air gaps at the corner joints and T-joints

because each layer is accurately positioned. This is more difficult with two layers

stacked together and almost impossible with three layers. Also having two or three

layers stacked in the same way causes increased joint losses, since the flux losses

increase significantly and hence the eddy current losses increase.

Fig. ‎1-8 Square joint

Fig. ‎1-9 350/550 Miter joint



14

Fig. ‎1-10 Mitred corners

Fig. ‎1-11 Step-lap joint



15

Fig. ‎1-12 450 Mitre joints

Cross-section of transformer cores 1.3.2

Transformer cores are built with different type of cross-sectional area, for example

cores build with rectangular cross-section as shown in Fig. 1-13 (A). This type of

cross section can be used for a small size transformer. Because it is wasteful to use

magnetizing coils for rectangular cross-sections. So square cores maybe used as

shown in Fig. 1-13 (B). But considerable amount of useful space is still wasted so a

common improvement on square core is to employ cruciform core as shown in Fig.

1-13(C), which demands at least two sizes of core strips [23]. However, for large

transformer core cross-section, more steps are used as shown in Fig. 1-13(D).



16

Fig. ‎1-13 Cross sectional area of transformer core – limbs

A

B C

D



17

Flux density harmonics 1.3.3

The overall flux density in transformer core is sinusoidal, but it is distorted in

individual layers [24]. In general harmonic mainly occur in the saturated regions

such as T-joint area [25]. However, circulating harmonics have also been

experimentally found in the limbs and yokes of transformers [26]. It is extremely

difficult to calculate the power losses due to harmonics.

Core performance 1.3.4

The first transformer was built in (1885) and the most important development was

initiated after the grain-oriented steel was made available for use in 1941 [27]. Early

experiments were carried out to compare the performances of the grain-oriented steel

with non-oriented silicon steel. It was found that the use of grain-oriented steel

resulted in approximately 20% reduction of core weight and 10 to 15% reduction of

iron losses.

In 1922 [28] the most extensive research carried out in recent years were an

investigation of magnetic distribution of three and single phase transformer

laminations, flux distribution and power loss in the mitred overlap and T-joints, flux

paths and flux transfer mechanism and measurements of rotating flux.

1.4 Power loss in silicon-iron transformer cores

When transformer core energised, alternating magnetizing current flows in the core

and this results in electrical power dissipated in form of heat within the cores [29].

This loss can be looked at as a result of two components, one due to the material and

the other due to the construction of the core.



18

Power loss due to core materials 1.4.1

Loss occurred due to the material is considered to be two types: hysteresis loss and

eddy current loss. Static hysteresis loss is the energy lost when magnetizing the

material around its magnetization loop and it is affected by its chemical composition

and the methods used in processing it [30].

Eddy current loss occurs when the material is magnetized in an alternating field, and

it is influenced by the electrical resistivity of the material and the thickness of the

lamination.

Power loss due to construction of the cores 1.4.2

Additional losses are introduced when building transformer core. These losses are

due to mechanical stresses, flux density harmonics, presence of joints, air gaps and

mechanical stresses.

In transformer core stresses are present and it is very difficult to eliminate them.

These stresses are introduced due to waving of lamination, bending caused by the

weight of laminations, clamping forces and temperature gradients due to non-

uniform distribution of flux density [31].

Magnetostriction in ferromagnetic material 1.4.3

The magnetic moment in ferromagnetic material lie in one direction. This alignment

leads to a strong interaction in magnetic domain as shown in Fig. 1-14. Hence,

ferromagnetic material can exhibit net magnetisation without applied external

magnetic field.



19

Fig. ‎1-14 Magnetic domain wall in ferromagnetic materials

First effect of the magnetostriction on ferromagnetic material was observed by Jule

[30]. If a low value of external magnetic field is applied to these domains, few

domains will change their direction to the applied filed in order to balance the

internal field to zero.

A second effect occurs during the magnetisation when increasing the external applied

magnetic field, these domains will rotate into the direction of the applied filed.

However, removing the external applied field forces the domain wall to move from

its original position to a new position and will not return to its original position due

to the domain wall pinning and due to the impurities of the material. Therefore, any

rearrangement of the domains result in changing the shape of the material. Fig. 1-15

b [32]. This change in magnetic domain induces strain in the material, and results in

change in the magnetostrictive strain, . The magnetostrictive strain can be positive

or negative depends on the material properties and applied magnetic field. If the

length of the material increased under external magnetic field this called positive

magnetostriction.

Changes occurred in the material can be calculate using equation:



20

=

(1.5)

Where L is the change in length and L is the original length of the material

Fig. ‎1-15 Effect of magnetostriction (a) zero field (b) applied field



21

Previous related work 1.4.4

There has been huge number of research studies carried out on transformer core

losses, core magnetostriction and core harmonic distribution under sinusoidal and

PWM voltage excitations.

Boglietti, Ferraris and Lazzari [29], measured power losses under sinusoidal and

PWM excitations using wound grain oriented transformer core. They found that

PWM caused higher power losses than sinusoidal. This increasing of the losses was

due to the high eddy current caused by PWM inverter.

Moses and Tutkun [33] investigated harmonic components under PWM and

sinusoidal and they found that total harmonic distortion (THD) was higher under

PWM. This was due to the complex flux waveform.

Basak and Moses [34], investigated the relationship between losses caused by low

harmonics order in the three-phase transformer core, they found that losses were

higher in the joints and the harmonic distortion was a major cause of power losses.

Basak and Abdul Qader [35] investigated (THD) in the three-phase transformer core

with high magnetising range, they found that the largest third and fifth harmonic

components were found in the central limb.

Neurath [36] has measured localised magnetostriction using displacement

transducers

In 1966 Brownsey [37] measured fundamental component of magnetostriction using

ceramic displacement transducer.

Anderson [38] has measured peak to peak magnetostriction in Epstein strip using

piezoelectric accelerometer.



22

Aims of the Investigation 1.4.5

Transformer represents the largest capital investment in the distribution section of a

power system and provides the best opportunity to make them more efficient

whenever possible. Since power is transformed from the generation station to the

consumer, the accumulative losses are significant, although transformer consume the

majority of a nation’s electricity and are the primary movers of manufacturing

industry, efficiently designed and built transformer core have resulted in significant

economic and productivity benefits, both to manufacturing industry and to the nation

as a whole. One of the most common electrical machines is the transformer, which is

universally highly used for industrial applications although there is a difficulty of

power loss and core noise.

The research about core loss began very early on in the life of the power transformer.

The improvement of the performance of such cores has come from improving basic

magnetic properties of core material and the advance in the production techniques

providing purer material with strong directional properties The efficient performance

of a transformer core not only depends on the quality of the material but also on the

core design. Some relevant work have been carried out previously but only when

transformer is energised through three- phase inverter under no-load condition.

In the present work, an attempt has been made on practical transformer core and on

the model cores to obtain deep knowledge of the flux behaviour. Moreover, studies

about localised power losses and stress and also the effect of clamping pressure on

losses under both on-load and no-load conditions, when transformer energised via

three-phase sinusoidal and PWM voltage excitation were performed. Within this

knowledge overall power loss of magnetic cores can be reduced and more efficient

transformer can be developed.

Moreover, increased environmental concern has called for low acoustic noise

produced by transformers. It is known that energy supply systems have undergone

some major changes due to the growing role of power electronic techniques in the

grid through power flow conditioners and converters of electricity. Therefore,

transformers subjected to PWM voltage excitation are becoming more common;

assessment and improvement in the performance of transformers under PWM



23

voltage excitation are increasingly prominent. This research project aims to

investigate the no-load and on-load performance of a model three-phase, three-limb

laminated transformer core, assembled from high permeability grain oriented steel

(HGO), operating under sinusoidal and PWM voltage excitations. Also, the main

aims of the investigation can be summarised as follows:

a). To measure localised magnetostriction of grain-oriented, 3% silicon electrical

steel in the form of three-phase transformer, using strain gauge method, to compare

and analyse the measurement results under sinusoidal and PWM voltage excitations,

and also to explain mechanical resonance phenomena in material subjected to PWM

voltage excitation.

b). To measure the total iron losses and localised flux density within the laminations

in transformer core joints using a computerised measurement system, to estimate

localised rotational and planar eddy-current losses under sinusoidal and PWM

voltage excitations, and to obtain a better understanding of the influence of

modulation index and switching frequency.

c). To measure localised bending effects and strain of the same model transformer

core, to compare and analyse the measurement results under sinusoidal and PWM

voltage excitations, and also to explain the magneto-mechanical resonance

phenomenon of the core under PWM voltage excitation.

d). To make an analysis of the results in order to draw general conclusions as to the

effect of PWM waveforms on loss, strain and flux distribution and quantify the

expected effect on transformer core efficiency in general.



24

CHAPTER 2

2. Type of the transformer core materials

Transformer core material is the significant part which may be made from various

types of electrical steel dependent on the type of the transformer. It is also dependent

on the cost of the electrical steel for example, in induction motors, the stator cores

are usually made from non-oriented steel to minimise the magnetic losses in the core.

On the other hand, transformer core is usually built from grain-oriented steel and

grain-oriented steel with laser scribed domain refined material to minimise the core

losses.

Grain oriented steel 2.1.1

The most important magnetic material used in large quantities in transformers and

sometimes in large rotating machines, is grain-oriented silicon steel which is

produced in different grades with their qualities assessed by iron losses. Therefore,

the use of grain-oriented steel is to reduce the production of iron losses. The losses of

the best oriented steel are about 70% less than the best grades of non-oriented steel.

Introduction of silicon into iron result in two important effects, firstly it decreases the

permeability of the material and second, it increases the resistivity. Therefore,

reducing eddy current loss. On the other hand, the presence of a large amount of

silicon in steel result in reducing the saturation magnetisation and it also makes the

steel harder and more brittle. In order to obtain optimum Si-Fe alloys, the silicon

content should not exceed 5%. [39]

Non- oriented steel 2.1.2

Non-oriented steels are very nearly isotropic. Their magnetic and mechanical

properties are approximately the same in all directions in the sheet. Two different

grades of this material are supplied non-oriented non-silicon steel and non-oriented

silicon steel. In the case of non-oriented steel when material is rolled, some degree of

texture is usually produced. Therefore, in non-oriented silicon steel both losses and

permeability are lower than non-oriented non-silicon steel. The non-oriented silicon

steels contain a range of silicon from about 0.5% to about 3.2% to increase the



25

resistivity of the steel. If the concentration of silicon is higher than 3.5%, the steel

cannot be rolled in acceptable conditions. Hence, the amount of silicon rarely

exceeds 3.2%. Permeability of the steel increases through making the steel purer and

the grain size larger. Electrical steel with the large grain size result in lower eddy

current losses but higher hysteresis loss.

Laser scribed domain refined (LDR) 2.1.3

The LDR is another material used to build transformer core and it was developed to

reduce core loss of the high permeability grain-oriented material (HGO) by reducing

the width of magnetic domains through means of laser irradiation. However, the laser

irradiation produces stress in the lamination which then creates discontinuous

domain structure. And this leads to increase of magnetostriction in the transformer

core. [40]



26

2.2 Transformer theory and performance

Ideal transformer was always chosen to study the theory of the transformer. Fig. 2-1

shows ideal single-phase transformer core, having primary and secondary windings

N1 and N2 respectively, wound around ferromagnetic core.

Fig. ‎2-1 Ideal single-phase transformer core [3]



27

Therefore, the voltage induced in primary winding is equal to the voltage induced in

secondary winding, the relationship between primary and secondary windings known

as numbers of turns ration defined as:

2

1

2

1

2

1

I

I

N

N

V

V [41] (2.1)

Where and are the primary and secondary voltages, and are the number of

turns, and and are the primary and secondary currents,

Measuring flux density in ideal core using Faraday’s law

dt

de

[41] (2.2)

Where is the flux in Webers ( and equal to B • Sd

Since no flux leakage in the ideal transformer core hence the instantaneous in

secondary winding is equal to

dt

dNe

22

[2] (2.3)

Therefore, the induced in the secondary winding by the flux variations is

given by.

dt

dt Ne

22

)( [2] (2.4)

As the flux is flowing continuously and changing its direction around the core, so to

find the flux density at any point of the core flux density could be found as:

A

ttB

)( [2] (2.5)

Where is the cross-sectional area of the core from equations (2.4) and (2.5) it can

be seen that



28

dt

tdBAN

dt

tdNte

)(2

)()( 22

[2] (2.6)

By using the above definition, the instantaneous flux density can be expressed as

dttAN

tB e )(1

)(2

2 [41] (2.7)

Overall flux density measurement under sinusoidal excitation 2.2.1

When the core is excited under sinusoidal waveform, the flux as function of time is

given by

ttpk

sin)( [41] (2.8)

Where is the peak flux, and is the angular frequency then the

secondary induced voltage in the transformer core is given by:

tNdt

tdt

pkNe

cos)(

)(2

22 [41] (2.9)

Therefore, the value of the secondary induced is given by

pkpkrmsfNfNe

22

44.42

2 [41] (2.10)

For an alternating and sinusoidal variation of flux density

tBtB pk sin)( [41] (2.11)

Where is the peak value of the core flux density, by introducing equations (2.5)

and (2.9), it can be shown that

tBANt pke cos)( 22 [41] (2.12)

So that the value of the secondary induced is also given by

BANferms pk244.4 [41] (2.13)



29

In order to determine the average value of the secondary induced voltage over a

period of time,

dttT

T

av ee )(2 2/

0 2 [41] (2.14)

Hence the average secondary induced voltage can be calculated from

BANf pkave 24 [41] (2.15)

Hence, for desired core flux density the corresponding induced voltage in the

reference search coil could be calculated using the equation (2.13). Moreover,

equation (2.15) can be used under sinusoidal voltage excitation. For this work,

equation 2.13 was used to determine the level of excitation of the core. Table ‎2-1

shows the required voltage to obtain desired flux density 0.4T, 0.6T and 1Tesla.

Therefore, the induced voltages in the search coil were measured using a Fluke

8050A Digital Multimeter type 8050A which had accuracy better than ±

%. The

overall flux density could therefore be set to within ± 1

%.

Table ‎2-1 Overall voltage calculation of desired peak flux density under sinusoidal excitation

B/Tesla (T)

e/ Volt

0.4

33.3

0.6

49.95

1

83.25



30

Overall flux density measurement under PWM voltage excitation 2.2.2

Power loss was measured under load and no-load conditions, in order to monitor the

induced voltage in the search coil both localised and overall. Integrator was used to

convert the voltage into magnetic flux density so that the induced voltage will be sine

waveform.

Due to the distortion generated by the PWM waveform, power loss induced in the

transformer core will be higher than those when transformer core is energised by

sinusoidal waveform. Using the fundamental equation in electromagnetism the

PWM waveform must be defined analytically, as PWM voltage waveform is a

discrete function therefore the definition can be given in a half cycle:

[42] (2.16)

Where n

i

1

are sum of pulse widths in a half cycle and is the inverter output

voltage. Therefore, the instantaneous flux density can be obtained from Faraday’s

law in discrete form as:

iNA

vdttv

NAtB )(

1)( [42] (2.17)

Where is the number of turns and is the cross-sectional area. When flux density

approaches its maximum at one cycle it can be expressed by:

Im NA

VB

2 [T] [42] (2.18)

Equation (2.18) was used to set desired value of the peak flux density in the

transformer core. Table 2.2 shows the required voltage to obtain desired flux density

0.4T, 0.6T and 1Tesla. However, in order to obtain the peak magnetic flux density in

transformer core it is important to know the number of turns in the overall search coil

and it is usual to use the middle limb as reference. Nevertheless, search coil must be



31

placed in the middle of the limb where the amount of flux flowing is highly through

that area. Second parameter that must be known is the core cross sectional area.

Table ‎2-2 overall voltage calculation of desired peak flux density under PWM excitation

B/Tesla (T) e/ (volt)

0.4 150

0.6 250

1.0 350

Fundamental theory of localised power loss measurement in transformer 2.2.3

cores

Power losses instantaneously dissipated in a single point of transformer cores

lamination under one dimensional magnetisation can be expressed by:

)(tP dvz

tHdv

t

tBtH

vv

2))(

(1

])(

)([

[w] [42] (2.19)

Where )(tH is the instantaneous magnetic field strength, t

B

is partial

differentiation of the flux density with time, dv is the differentiation of the volume,

is conductivity of magnetic core material and z

tH

)(is partial differentiation of

the magnetic field strength with one dimension of the transformer core. Hence,

averaged power loss over one cycle can be obtained from:

dtdvz

tHdv

dt

tBtH

T

T

v v

averageP

0

2))(

(1)(

)(1

[W] [42] (2.20)



32

By re-arranging equation (2.20) averaged total power losses can be expressed as:

dvdtz

tH

Tdvdt

t

tBtH

T

T

v

T

V

averagedP2

00

))(

(11)(

)(1

[W] [42] (2.21)

If magnetic field strength and magnetic flux density are assumed to be uniform

within volume v , that is magnetic field strength and magnetic flux density change

with only time, then ( ))(

z

tH

will be zero and

t

tB

)(will be defined as

dt

tdB )(. Hence,

averaged total power loss under one dimensional magnetisation can be written as:

dtdt

tdBtH

Tm

vT

totalP ])(

)([1

0

[W/kg] [42] (2.22)

Where and dttdB /)( are volume of the magnetic core, mass of the

material, magnetisation period, instantaneous magnetic field strength and the rate of

change of flux density with time respectively.

Total iron losses using loss separation criteria 2.2.4

Recently, several methods have been approached to calculate total iron losses under

PWM waveform such as (Amar) [42] shows to predict total iron losses under PWM

excitation in Epstein strips using separation method. Dividing iron losses into three

parts which are hysteresis losses, eddy current losses and excess losses, total iron

losses under PWM voltage excitation can be expressed by:

5.0

5.1

0

22

)(

24

3

2

i

m

i

m

htot

BBPP M

AGV

m

d

[W/kg] [42] (2.23)

Where is hysteresis loss, is conductivity of the material is the thickness of the

lamination sheet is a dimensionless coefficient. Total power loss under PWM

excitation is dependent on the total number of pulses in a half cycle for example as

the pulses increase losses decrease. However, in order to show the difference



33

between frequency dependent total loss under PWM and sinusoidal excitations iron

losses under sinusoidal excitation can be expressed as:

5.15.1022

22

2

6f

m

AGVf

m BBd

PP pkmhtot

[W/kg] [42] (2.24)

Where is the magnetising frequency. The form factor coefficient of PWM voltage

is ratio of the form factor of the PWM voltage and sinusoidal voltage, = 2/

( √ ). If the dynamic losses in equation (2.24) are multiplied by this term under

the condition of the PWM voltage excitation with respect to sinusoidal voltage

excitation (where the total iron losses under PWM voltage excitation

rewritten as:

f

f

ffP

i

ex

f

cl

i

htot

PP

P

)(2

41

)(

sin

)(sin

2

[W/kg] [42] (2.25)

Where is the hysteresis loss, is eddy current losse, and is the excess losses

respectively. Moreover, as the number of pulses per half cycle is the most important

parameter in the PWM which influences the power loss to increase, this is can be

controlled by control voltage frequency and the carrier frequency. If the ratio of these

two frequencies is large than the number of pulses will be high. Therefore, the losses

are expected to decrease.

2.3 Hysteresis losses

As shown in Fig. 1-2 hysteresis loss is proportional to the area enclosed by the loop

hysteresis losses occur in ferromagnetic material such as iron or steel. For example,

When ferromagnetic material is subjected to external magnetic field the hysteresis

loop will appear, it is also known as B-H loop or B-H curve [43]. When a low

external magnetic field is applied to magnetise a pure specimen of ferromagnetic

material it will result in changing the material properties as some of domain walls

will follow in the direction of the applied field and some will direct to random



34

direction. When the external field is increased, all domain walls will align into the

applied field. However, when the external applied field is removed, domain walls

will not return to their first pattern so induced magnetising element will remain in the

material because ferromagnetic material have high coercivity that is hard to

demagnetise. A coercive field has to be applied to bring the saturation value (Mo) to

zero. If the external field increased again, magnetic path will follow into the negative

side of the curve and hence one full cycle has been obtained which is proportional to

the power losses per one cycle[44].

Table ‎2-3 saturation value of some material [3,5,6]

Saturation value of the material

Material Saturation magnetisation. Mo [T]

Iron

2.15

Cobalt

1.78

Nickel

0.60

3% silicon Iron

2.03

There are several methods that have been developed to study hysteresis losses, such

as Jiles Atherton [44] method and Preisach method. Each method is based on

different estimation, for example Jiles Atherton studied the physical mechanisms in

ferromagnetic materials such as (magnetic domains, domain wall pattern and pinning

sites). Whereas, Preisach method is known as the mathematical method disregarding

the physical background. However, they are adapted methods for predicating the

hysteresis loss. Steinmetz method has also been used to calculate hysteresis losses.

His method depends on the peak flux density and experimental coefficients. Using

Steinmetz method, hysteresis losses can be written as:

BPn

mhk [ ] [42] (2.27)



35

Where k and are experimental constants which are dependent on the magnetic

material. Therefore, by substituting equation (2.18) into equation (2.27), hysteresis

loss can be written as:

NA

VkPh 2

i [ ] [42] (2.28)

By the identification of the unknown constant for the magnetic material tested under

the PWM voltage waveform in an electromagnetic circuit, hysteresis losses can be

predicted using equation (2.28).

Eddy current losses 2.3.1

Eddy current loss component is proportional to the magnetising frequency and is

dependent on the thickness of the lamination. If the lamination is thick and has small

grain oriented, exiting current is low to give peak flux density, as the transformer

core is made from conducting material and when the core is energised, alternating

flux flows through the core. This flux will induce an electromotive force

voltage according to Farady’s law.

This induced voltage causes currents to circulate through the magnetic core

according to Ohm`s law. These “eddy currents” produce heat in the core and as a

result power loss takes place in the core. The eddy current loss under PWM

excitation can be calculated by:

dtdtdBTm

fdT

clP 0

22

)/(1

)12(

[W/kg] [42] (2.29)

Where is conductivity of the material, is density of the material, is the

thickness of the lamination and

is the rate of changing flux density with changing

time, as the rate of changing flux under PWM excitation is constant and equal to

in half cycle. However, when the output voltage of the inverter is not zero by

replacing

with

in equation (2.29) eddy current loss can be expressed as:



36

fm

df

i

m

icl

BP

2

2

3

2),( [W/kg] [42] (2.30)

As the eddy current loss under PWM excitation depend on number of pulses in half

a cycle and the magnetising frequency. Hence in order to decrease eddy current

losses under PWM excitation the number of pulses per half cycle should be made

high, this is obtained by increasing the carrier frequency modulation index as well as

choosing a thinner material.

Anomalous loss 2.3.2

When external magnetic field is applied to a transformer core, domain walls start

moving and obeying the external field by rearrange themself toward the external

field. This domain wall motion leads to increase excess loss. According to (Bertotti),

excess losses are the difference between the measured total losses and the sum of

hysteresis losses and eddy current losses and can be expressed as:

dt

dBhP eex

[W/m3] [45] (2.31)

Where is the damping field generated by the excess eddy currents. It also assumed

that the change of magnetisation is accomplished, at a given time t through the

reversal of active regions, so called “magnetic objects” randomly placed in the

sample cross section.

As the lamination of the transformer core made with the fine material, domain walls

strongly associated together so magnetisation process will thus proceed according to

the distribution of the domain walls will produce dynamic balance between the

external filed and the domain walls that can be expressed as; induction rate

and

eddy current counter-fields. Any variation of

entails a variation in such a balance,

on the basis of the analysis developed through equation (2.22), Hence, the excess

damping field can be defined as:

)(

1

tndt

dBGS

xeh [A/m] [45] (2.32)



37

Vh

no

e

xt )( [45] (2.33)

Where is the conductivity of the materials is the cross-sectional area and and

were determined from the previous experiments carried out by Bertotti. They

were found to be 0.1356 and 0.15 A/m for 3% Grain-oriented and 0.1356 and 0.12

A/m for 3% Non-oriented laminations respectively [45]. By combination of

equations (2.32) and (2.33) the instantaneous excess power loss can be expressed by

dtdt

dB

Tm

AGV TO

exP5.1

0

1

[W/kg] [45] (2.34)

If

is replaced with

then equation will be rewritten as

5.0

5.15.1

)(

24

i

mO

ex

f

m

AGV BP

[W/kg] [45] (2.35)

Determined and from the magnetic material excess losses under PWM

voltage waveform can be calculated from equation (2.35). Nevertheless, all these

equations can be used to predict total iron losses under PWM voltage excitation in

grain oriented or non-oriented electrical steel.



38

Theory of estimates of iron loss components using loss separation criteria 2.3.3

The total iron loss can be divided into three groups using loss separation criteria

which can be expressed as:

P = )(2 fff PKK anedh [45] ( 2.36)

Where K h is the hysteresis loss constant, K ed

is the eddy current loss constant and

Panis the anomalous loss which is frequency dependent dividing equation 2.36 by

the magnetising frequency we obtain

f

ff

f

P PKK

an

edh

)( [45] (2.37)

In order to determine K h, the total loss is measured at different frequencies at

constant peak flux density and then the measured total power loss is divided by the

magnetising frequency in each case.

Estimates of loss components can be also obtained using Bertotti’s model. The

general Bertotti’s model can be written as a frequency dependent function of form

2/32 fff KKKP exbedbhbb [W/kg] [45] (2.38)

Where K hbis the hysteresis loss constant, K edb

is the eddy current loss constant and

K exbis the anomalous loss constant. Dividing both sides by f we can obtain specific

loss per cycle which can be written as:

2/1fff KKK

Pexbedbhb

b [45] (2.39)

Where K hb is the hysteresis loss per cycle, fK edb

is the classical eddy current per

cycle and 2

1

fK exb is the excess loss per cycle respectively.



39

Flux density distribution 2.3.4

Flux density distribution will be examined in great details throughout the cores. Both

overall and localised flux densities were measured. One layer of the core lamination

was removed and prepared to study localised distribution at T-sections, corner

sections, and in the middle of the limbs and the yokes as shown in Fig. 2-2. Overall

flux density of the core was also studied through the limb and yoke as shown in Fig.

2-3. The effect of clamping pressure and the variation of magnitude and phase angles

of flux density will be examined in great details.

Fig. ‎2-2 Positions of the localised search coils



40

2.4 Overall flux density distribution under sinusoidal voltage excitation

In order to measure overall flux density distribution in transformer core, search coil

technique was used which is also known as reference search coil technique. Two

search coils were wound around the limb and yoke Fig 2-3 illustrates the positions of

the search coils. The width of the limb was 0.0075 cm and that of the yoke. The core

was energised over a range of different peak flux densities of 0.4T, 0.6T and 1.0T.

Study of the overall flux density distribution has been obtained over every range of

magnetising peak flux density for example at 0.4 T, under load condition the flux

density in the yoke was 1.5% higher than that of the limb. Whereas, at 0.6 T, the

flux density in the yokes had a value of 1.6% higher than that in the limb. However,

when the core was energised at 1.0T, flux density in the limbs was 2% higher than

this in the yoke.

It can be observed that energising the core at higher level of flux density 1.0T, the

overall flux density in the yokes started to decrease and became lower than that of

the limb. Whereas when the core energised at 0.4T and 0.6T, flux density in the yoke

was higher than that in the limb. Furthermore, measurements of the overall flux

density were taken under load and no-load conditions, and results have shown those

overall flux densities are close to each other under load and no-load conditions. Fig.

2-4 shows overall flux density in the limb and Fig. 2-5 shows overall flux in the yoke

when the core was energised at 0.4T. Table 2.4 summarise overall distribution

in the three-phase transformer core.



41

Fig. ‎2-3 Position of the reference search coils

Table ‎2-4 Induced B ( ) in the reference search coil

(T) Limb ( ) Yoke ( ) Percentage

0.4

5.91

6.00

1.5%

0.6

9.03

9.18

1.6%

1.0

10.58

10.35

2%



42

Fig. ‎2-4 Variation of the induced voltage against time under sinusoidal waveform in the

transformer limb at 0.4T

Fig. ‎2-5 Variation of the induced voltage against time under sinusoidal waveform in the

transformer yoke at 0.4T



43

Overall flux density distribution under PWM voltage excitation 2.4.1

In order to adjust output voltage of the inverter integrator circuit must be

implemented to change pulse signal to sine signal. Fig. 2-6 is showing voltage

signals before integrator circuit and Fig. 2-7 shows PWM signal after integration.

However, when transformer core was energised by PWM voltage waveform,

transformer core was subjected to additional losses due to PWM flux distortion.

Fig. ‎2-6 variation of the overall flux density against time (ms) before the integrator circuit

Fig. ‎2-7 variation of the overall flux density against time (ms) after integrator circuit



44

Instantaneous PWM has spikes on its waveform. At high switching frequencies, the

PWM has less distortion because of the increase in the number of pulses per cycle.

When the core fed by PWM voltage excitation at 0.4 T, under load condition the flux

in the limb was 11% higher than that in the yoke. However, when the flux density

was increased to 0.6 T, flux density in the limb was 6% higher than that of the yoke.

Further increase in the peak flux density to 1.0 T, flux density in the limb was higher

than those of the yoke by a factor of 10%.

It could be noticed that the flux density in the limb was higher than those of the yoke

when the core energised under 0.4 T, 0.6T and 1.0 T. Similar results were obtained

under no-load condition.

Flux density in the limb was always higher than those in the yoke at all magnetising

levels and that has led to higher temperature rise in the limbs rather than that in the

yoke. Temperature gradients could also occur in areas near the joint producing

stresses in the laminations, table 2.5 summarise overall occurred in the limb and

in the yoke.

Table ‎2-5 Variation of fundamental components of overall flux density in the limbs and yokes

Core excitation

Limb (T) Yoke (T) Percentage

0.4

0.42

0.37

11%

0.6

0.73

0.68

6%

1.0

1.10

0.98

10%



45

Field and flux measurement method 2.4.2

In order to measure localised power loss it was required to measure magnetic field

and so the measurement technique was decided upon the requirement need.

Magnetic field measurement 2.4.3

For the measurement of magnetic field induction, it was decided to use a

conventional search coil method. The search coils of 0.1mm wound around a

common non-magnetic former and then number of search coil was chosen to one turn

for both and directions.

H -coil construction and calibration 2.4.4

The H-coil was made from enamelled copper wire, wound around a common non-

magnetic former with precise dimensions of (25 mm 25 mm 0.3 mm). The

number of turns of the coil and the diameter of the wire were 500 turns and 0.1 mm

respectively. Many turns of H -coils were wound to produce a large

proportional to dH/dt, to produce a high signal to noise ratio. Fig 2-8a. The H-

coil was calibrated in a range of known sinusoidal magnetic field produced inside a

1.15 m long, 729 turns uniformly wound air cored solenoid with 1.5 mm wire

diameter. H-coil was positioned at the centre of the solenoid core, where the

magnetic field is uniform and constant. The H – coil calibration set up used is shown

in Fig. 2-8a and 2-8b the output voltage o form the H coil was measured for

different magnetising currents. Equation 2.37 was used to calculate the field strength

H values for different magnetising currents. Graphs of H versus o were plotted.

Output signal form the H and o coil was connected to a “Fluke 115 true multi-

meter” for the processing of magnetic signal [46].

H

(2.37)

Where N = number of turns in the magnetising winding

I, L = magnetising current and mean magnetic path length respectively



46

Fig. ‎2-8 Schematic diagram of solenoid system



47

Table ‎2-6 Output voltage and current from solenoid core

Applied voltage

Detected voltage

H =

24

3.28 15.2 2079

33

4.47 21.9 2833

58

7.94 24.5 5033

Fig. ‎2-9 Voltage vs magnetic field with assign value of flux density

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 2000 4000 6000 8000 10000

Vo

(m

V)

H A/m



48

CHAPTER 3

3. Pulse width modulation (PWM)

Historically AC motors have fixed frequency which is 50 Hz or 60 Hz.

Developments in the technology of power electronics have provided inverters with

different voltage and different frequency level usually in the range between 0 to 500

Hz. Three-Phase static converters (PWM), are usually used in commercial and

domestic applications which are found in air conditioners, dryers, and many other

applications [47, 48]

The output voltage of (PWM) is obtained by comparing a reference voltage

waveform usually sinusoidal and carrier voltage waveform, usually triangular ( Fig

3.1). Reference voltage frequency usually in the range 0 to 100 Hz, and the carrier

voltage is usually between 1 kHz to 22 kHz. PWM has two parameters which

determine its output performance, modulation index and switching frequency.

Fig. ‎3-1 . PWM waveform generators [3]



49

Modulation index 3.1.1

Modulation index and its range is one significant parameters that determines the

output voltage of the PWM inverter. The amplitude of the fundamental frequency

component of the output voltage varies linearly with modulation index

provided that modulation index range is between 0 and 1. Therefore, range of the

modulation index from 0 to 1 is referred to as linear range. However, if the

modulation index is larger than 1.0 the peak value of exceeds the peak value

of and this will cause large harmonic contents in the PWM output voltage.

Modulation index defined as:

=

(3.1)

Where is the sinusoidal signal and is the carrier voltage signal as shown

in Fig. 3-1. Then the output voltage will depends on the circuit configuration [49]

Switching frequency 3.1.2

PWM has two frequency components which are switching frequency and

fundamental frequency. The inverter switching frequency is generally kept

constant with triangular waveform .Whereas, the fundamental frequency

is used to modulate the switch duty ratio and is kept constant with sinusoidal

voltage signal. The ratio between switching frequency and fundamental frequency

is defined as frequency modulation ratio and equal to:

=

(3.2)

It is desirable to use as high a switching frequency as possible. Moreover, switching

losses with the inverter increase proportionally with the switching frequency because

of the relative ease in filtering harmonic [49]. It is also desirable to use as high a

switching frequency as possible because of the advantages of no audible noise with

switching frequency of 20 kHz or greater than 20 kHz [50].



50

Voltage source inverter 3.1.3

The three-phase inverters consist of three legs, one leg for each phase and are

commonly used to supply three-phase loads as shown in Fig. 3-2. Each phase voltage

has 0120 phase angle between them, therefore the conduction sequence is given as:

, , , , , and . The output volatge is independent of the

output load current since one of the two switches in each leg is on at any instant [49].

Fig. ‎3-2 Three-phase PWM inverter voltage configuration circuit [4]



51

Current source of PWM inverter 3.1.4

One important parameter of the PWM inverter that has been studied in this section is

its use as current supply source. The PWM inverter consists of three elements

(thyristors, capacitors, and diodes). To control three-phase current circulation each

thyristor is used to switch the current element on by firing a pulse on its gate whereas

capacitors and diodes are used to turn the current off. The force commutation circuit

works in such a way that firing an incoming thyristor automatically commutates the

outgoing thyristor. This force is known as auto sequential commutation. Fig. 3-3

shows circuit diagram of controlled current [49]

Fig. ‎3-3 Schematic diagram of controlled current S1, S2 Switch. L: Inductance R:

Resistor [1]



52

3.2 Magnetizing current variation under PWM voltage excitation

In order to detect the current flowing in the three-phase inverter, three 1 Ω power

resistors were coupled parallel to the three-phase inverter. The outputs of the

resistors were connected to the DAQ card. Detection of each phase current signal

was taken through “Lab-View” programme. The core was energised over different

range of peak flux density 0.3T, 0.4T and 0.7T respectively. During the

measurements, switching frequency was varied in the range of 2 kHz, 3 kHz, 12 kHz

and 16 kHz. Measurements were taken under load condition and transformer was

connected in star configuration. Fig. 3-4 shows block diagram for measuring

magnetising current.

Fig. ‎3-4 Block diagram for measuring magnetising current



53

Fig. 3-5 shows variation of the magnetizing currents with flux density in the outer

limb under PWM voltage excitation with assigned value of switching frequency. To

obtain a flux density of 0.3T at switching frequency of 2 kHz and 3 kHz, the current

required was 0.1144amps. Whereas, at switching frequency of 3 kHz, current needed

was 0.1108amps. However, for the middle limb current needed at switching

frequency 2 kHz and 3 kHz were 0.1087amps and 0.1062amps respectively, as

shown in Fig. 3-6.

Fig. ‎3-5 Variation of magnetizing current at 0.3T in the outer limb with assigned values of

switching frequency (kHz)

Fig. ‎3-6 Variation of magnetizing current at 0.3T in the middle limb with assigned values of


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

fs 2kHz fs3 kHz

Ma

gn

etsi

ing

cu

rren

t Ir

ms

(A)

0

0.02

0.04

0.06

0.08

0.1

0.12

fs 2kHz fs 3kHz

Ma

gn

etiz

ing

cu

rren

t Ir

ms

(A)



54

When the peak flux density was increased to 0.4T current needed in the outer limb at

switching frequency 2 kHz was 0.139amps. Whereas, at switching frequency 3 kHz

current needed was 0.1164amps as shown in figure 3-7. However, for the middle

limb current needed at switching frequency 2 kHz was 0.112amps and for 3 kHz

current required was 0.1091amps as shown in Fig. 3-8 respectively.

Fig. ‎3-7 Variation of magnetizing current at 0.4T in the outer limb with assigned values of


Fig. ‎3-8 Variation of magnetizing current at 0.4T in the central limb with assigned values of


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

fs 2kHz fs 3kHz

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)

0

0.02

0.04

0.06

0.08

0.1

0.12

fs 2kHz fs 3kHz

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)



55

When the switching frequency was increased to 16 kHz and 12 kHz to obtain flux

density of 0.7T current required in the middle limb was 0.1833 amps and 0.1869

amps respectively as shown in Fig. 3-9.

Fig. ‎3-9 Variation of magnetising current at 0.7T in the middle limb with assigned values of


Fig. 3-10 illustrates the current needed in the outer limb to obtain flux density of

0.7T at switching frequencies 16 kHz and 12 kHz were 0.1854amps and 0.1887amps

respectively.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

fs12 fs16



56

Fig. ‎3-10 Variation of magnetising current at 0.7T in the outer limb with assigned values of


Therefore, at all magnetizing levels at low switching frequency ( ) PWM

waveform requires more current than that at high switching frequency. Nevertheless,

at low switching frequency audible noise is high and that will lead to increased

vibration in the transformer core. Hence, magnetostriction will increase the

advantages of increasing switching frequency to 16 kHz or greater is the absence of

audible noise.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

fs12 fs16



57

Magnetizing current variation under sinusoidal voltage excitation 3.2.1

Digital power analyser was used to study the variation of the magnetising current.

When the core was excited via three-phase variacs, measurements were taken under

load and no-load conditions. Table 3.1 and table 3.2 show current needed to obtain

desired value of the peak flux density 0.3 T, 0.4 T and 0.7 T. In the outer and central

limb and Fig. 3-11 to Fig. 3-16, shows the variation of magnetizing current with peak

flux density in an outer and central limb.

To obtain a peak value of 0.3 T under no-load condition, currents required in the

outer and central limb were 0.095 and 0.074 respectively. Whereas, currents

required at 0.3 T peak flux density in the outer and central limbs under load

condition were 0.4663 and 0.3879 respectively. However, increasing the flux

density to 0.4 T under no-load condition currents required in the outer and central

limb were 0.120 and 0.094 respectively. Furthermore at 0.4 T under load

condition currents required in the outer and central limb were 0.5869 and 0.5093

respectively. Further increasing the peak flux density to 0.7T under no-load condition

current required in the outer limb was 0.201 Whereas, in the central limb current

required was 0.187 . On the other hand, under load condition at 0.7 T currents

required in the outer and middle limb were 1.4804 and 1.2738 respectively.



58

Table ‎3-1 Current required for desired flux density under no-load condition

Outer Limb

(Amp)

Central Limb

(Amp)

Outer Limb

(Amp)

0.3T

0.095

0.074

0.095

0.4T

0.120

0.094

0.120

0.7T

0.201

0.187

0.201

Table ‎3-2 Current Required for Desired Flux Density under Load Condition

Outer Limb

(Amp)

Central Limb

(Amp)

Outer Limb

(Amp)

0.3T

0.466

0.387

0.466

0.4T

0.586

0.509

0.586

0.7T

1.480

1.273

1.480



59

Fig. ‎3-11 Variation of magnetising current under three-phase varaic under no-load condition at

0.3T

Fig. ‎3-12 Variation of magnetising current under three-phase varaic under load condition at

0.3T

1 2 3

0

0.02

0.04

0.06

0.08

0.1

0.12

Ma

gn

etiz

ing

cu

rren

t Ir

ms

(A)

Phase 1 Phase 2 Phase 3

1 2 3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)




60


Condition at 0.4T

Fig. ‎3-14 Variation of magnetising current under sinusoidal voltage excitation under Load

Condition at 0.4T

1 2 3

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)


1 2 3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)




61


Condition at 0.7T

Fig. ‎3-16 Variation of magnetising current under sinusoidal voltage excitation under load

Condition at 0.7T

1 2 3

0

0.05

0.1

0.15

0.2

0.25

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)


1 2 3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Ma

gn

etis

ing

cu

rren

t Ir

ms

(A)




62

Therefore, at all levels of magnetizations under both conditions, currents in the outer

limbs of the Three-phase transformer core were higher than those in the central limb

at 0.3T, 0.4T and 0.7T in the range of 68% to 97%, this was due to the asymmetry of

the magnetic path.

Comparison of the results 3.2.2

As it has been shown in Fig. 3-5 to Fig. 3.10, under PWM voltage excitation at low

switching frequency, current is higher than those at high switching frequency.

However, comparing the result obtained under both PWM and sine waveform,

current variation at 0.3T was higher under sinusoidal excitation than those under

PWM excitation in the outer and central limb.

At 0.3 T in the other limb, current variation under PWM excitation was higher than

those under sinusoidal excitation by the factor of 83%. Furthermore, at the middle

limb current variation under PWM excitation was higher by the factor of 68%.

Increasing the flux to 0.4 T, current variation under PWM excitation was higher than

sinusoidal excitation in the outer limb by 86%, whereas in the central limb it was

higher under sinusoidal by the factor of 83%.

At 0.7 T, current variations under PWM excitation recorded higher value than those

under sinusoidal excitation, in the outer limb it was higher by the factor of 92%.

Whereas in the central limb it was again higher by the factor of 97%. Comparison of

the measurement result is shown in table 3.3.



63

Table 3.3 Comparison of the Current measurements under sinusoidal and PWM voltage

excitation in the central and outer limb of the module Three-phase transform core

It could conclude that under all magnetising level variation current under PWM

excitation was higher than those under sinusoidal excitation. However, agreement

has been obtained from these experiments. Under all level of magnetising current

under both sinusoidal and PWM voltage excitation outer limb shows higher value

than the central limb this was due to the asymmetry of the magnetic path.

T

Sin waveform PWM waveform Percentage

Outer Central Outer Central

Sin PWM

0.3 0.095 0.074 0.1144 0.1087 22% 4%

0.4 0.120 0.097 0.139 0.112 19% 19%

0.7 0.201 0.187 0.1887 0.1869 6% 0.9%



64

Effect of switching frequency on overall flux density 3.2.3

One significant parameter that determines the output voltage of the PWM inverter is

a switching frequency. Switching frequency and its effect on overall flux density

distribution has been studied in detail throughout this work. Switching frequency was

varied in the range 2 kHz, 3 kHz, 8 kHz, 12 kHz, and 16 kHz. Single turn search coil

was wound around the limb and around the yoke and then single measurement was

taken separately for each switching frequency. Transformer core was energised with

different peak flux density 0.4T, 0.6T and 1.0T. Measurements were taken under

load and no-load conditions using “Lab-View” program as shown in chapter 4. Fig.

4-4.

When transformer core energised at peak flux density of 0.4T under no-load

condition at switching frequency 2 kHz, the overall induced voltage was

5.627 . Increasing the switching frequency to 3 kHz, overall induced voltage

was 5.126 . Energising the core with the same peak flux density of 0.4T under

load condition at switching frequency 2 kHz, overall induced voltage was found to

be 6.486 , while increasing the switching frequency to 3 kHz, overall induced

voltage was 5.417 ,

Energising the core with 0.6T under no-load condition at switching frequency 3

kHz overall induced voltage was 7.158 , decreasing the switching frequency to

2 kHz overall induced voltage was 8.056 . However, when measurements were

taken under load condition at = 2 kHz and = 3 kHz overall induced voltage was

6.486 and 9.475 .

Increasing the energising flux to 1.0T under no-load condition at 16 kHz, overall

induced voltage was 13.343 , reducing the switching frequency to 12 kHz, overall

induced voltage was 13.577 . However, when the core was energised at same peak

flux density under load condition at switching frequency of 16 kHz, overall induced

voltage was 13.039 , decreasing the switching frequency to 12 kHz, overall

induced voltage was 13.135 . Further decrease of the switching frequency to 8

kHz, resulted in having an overall induced voltage of 13.425 ,



65

Fig. ‎3-17 Overall induced voltage under PWM voltage excitation (no-load conditions) with

switching frequency varied from 2 to 3 kHz at different peak flux density (T)

Fig. ‎3-18 Overall induced voltage under PWM voltage excitation (load conditions) with

switching frequency varied from 2 to 3 kHz at different peak flux density (T)

0

1

2

3

4

5

6

7

8

9

SF2 SF3

Ov

era

ll i

nd

uce

d v

olt

ag

e (m

v)

0.4T

0.6T

fs3 kHz fs 2kHz

0

1

2

3

4

5

6

7

8

9

10

SF2 SF3

Ov

era

ll i

nd

uce

d v

olt

ag

e (m

v)

0.4T

0.6T

fs 2 kHz fs 3kHz



66


switching frequency varied between 8, 12, 16 kHz at different peak flux density (T)


switching frequency varied between 12, 16 kHz at different peak flux density (T)

Therefore, at all magnetising levels, the induced voltages under low switch

frequencies were higher than those at high switch frequency.

0

2

4

6

8

10

12

14

16

fs 8kHz fs 12 kHz fs 16kHz

Ov

era

ll i

nd

uce

d v

olt

ag

e (m

v)

1.0T

0

2

4

6

8

10

12

14

16

fs 12 kHz fs 16kHz

Ov

era

ll i

nd

uce

d v

olt

ag

e (m

v)

1.0T



67

3.3 Overall power losses under sinusoidal waveform

Three-phase power analyser “Norma D6000 (S/N: ND 58172 RR)”, was set to

measure total power losses under sinusoidal voltage excitation under load and no-

load conditions. Torque wrench was used to select desired clamping pressure on the

core which was varied in the range of (0, 8, 15, and 27 N/ 2). Moreover, overall flux

density was varied respectively in the range of (0.3T, 0.4T and 1T). Total power loss

formula used was:

= (3.3)

Where is the current and is the voltage. In this experiment the number of turns of

the primary and secondary windings were 50 each. In other word, the turn ratio of

this transformer is equal to one. Hence, since the number of turns of the primary and

secondary are the same ( = ), the induced voltage in the secondary winding is

equal to the voltage on the primary winding ( In the power analyser

measurement system, primary current ( ) and secondary voltage ( ) of the

transformer were used.

Setup of the measurement of overall power loss 3.3.1

Fig. 3-21, shows a picture of the measuring system which includes three single-

phase variacs with star connection, used to magnetise the transformer core. A digital

multi-meter was used to measure the output voltage of the single turn search coil and

a digital three-phase power analyser was used to measure the overall power loss. The

transformer core is made by highly grain-oriented material HGO and the laminated

core was compressed together with three non-magnetic clamping bars. The total

mass of the core was 96.1 0.01 kg. The primary and secondary windings were all

connected in star- star ( -λ) configurations. Tables 3.3 to 3.4 and graphs 3.22 to 3.30

shows the total power losses under load and no-load conditions



68

Fig. ‎3-21 Overall power loss measurement system

Table 3-3 Overall Power under No-load condition

(T) Clamping pressure

(N/ 2)

W/kg

0.4

0 0.41

8 0.45

15 0.47

27 0.48

0.6

0 0.57

8 0.78

15 0.87

27 0.88

1

0 1.22

8 1.24

15 1.19

27 1.18



69


flux densities


flux densities

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.6T 1.0T 0.4T

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.4T 0.6T 1.0T



70

Fig. ‎3-24 Overall power loss at clamping pressure of 15 N/ 2 under no-load condition at

different flux densities

Fig. ‎3-25 Overall power loss at clamping pressure of 27 N/m2 under no-load condition at

different flux densities

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.4T 0.6T 1.0T

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ov

era

ll p

ow

er l

oss

es (

W/k

g)

0.4T 0.6T 1.0T



71

Table 3-4 Overall power loss under load condition

(T) Clamping pressure

(N/ 2)

W/kg

0.4

0 0.51

8 0.54

15 0.56

27 0.57

0.6

0 0.77

8 0.82

15 0.91

27 0.92

1

0 1.20

8 1.34

15 1.17

27 1.16



72

Fig. ‎3-26 Overall power loss at clamping pressure of 0 N/m2 under load condition at different

flux densities

Fig. ‎3-27 Overall power loss at clamping pressure of 8 N/m2 under Load Condition at different

flux densities

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.4T 0.6T 1.0T

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.4T 0.6T 1.0T



73

Fig. ‎3-28 Overall power loss at clamping pressure of 15 N/ 2 under load condition at different

flux densities

Fig. ‎3-29 Overall power loss at clamping pressure of 27 N/m2 under load condition at different

flux densities

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4 O

ver

all

po

wer

lo

ss (

W/k

g)

0.4T 0.6T 1.0T

0.4 0.6 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.4T 0.6T 1.0T



74

Effect of clamping pressure 3.3.2

Pro Dial torque wrench was used to set desired clamping pressure on the transformer

core, the effect of the clamping torque was monitored on three-phase power analyser

“Norma D6000 (S/N: ND 58172 RR)”. When the clamping pressure was changed

from zero to 8N/m2, its effect at low flux density was to increase the exciting current

by 1.3% to keep the flux density constant. At the higher clamping pressure of

15N/m2 further increase of 3.8%, was required to maintain same flux density. On the

other hand, when the core was operated at 1.0T the exciting current had to be

reduced with increasing clamping pressure. A reduction of 2.6% was observed with

the clamping pressure increased from zero to 8N/m2.

The effect of clamping pressure on power loss is shown in tables 3.3 and 3.4 and Fig.

3-22 to Fig. 3-29. At low magnetic flux density, an increase of power was observed.

At high flux density of 1.0T, a reduction in power loss was obtained under load and

no-load conditions as shown in tables 3.3 and 3.4.

So it could be concluded that, at higher flux density and higher clamping pressure,

power loss decreased. That may be due to the fact that higher pressure improves flux

transfer in the corner and at T-joint regions by reducing interlaminar gaps and hence

reduces the loss in the joints.



75

Analysis and discussion 3.3.3

As it has been shown in the tables 3.3 and 3.4 at all level of peak flux densities and

under all levels of clamping pressure, overall power losses were higher under load

condition than that under no-load condition.

At 0.4T 0 N/m2, the variation in power losses was higher under load condition than

no-load condition by 19%. Increasing the clamping pressure to 8 N/m2, the variation

in overall power loss was higher by 16% under load condition. Further increase in

clamping pressure to 15 N/m2again overall power loss was higher by 16%. More

increasing of clamping pressure, power losses variation was kept a same percentage

difference.

Hence, it could be concluded that, the effect of varying clamping pressure on power

loss as shown in Fig. 3-22 to Fig. 3-29 an increasing of power loss was observed

when the clamping pressure was increased from 0 M/m2

to 8 M/m2.

However,

further increasing of clamping pressure from 15 N/ to 27 N/ . Power losses

decrease.

Order harmonic content with a change in peak flux density 3.3.4

Harmonic content of the primary current for peak flux densities of 0.4T and 1.0T was

examined. The result of the primary current from a sinusoidal excitation can be seen

in Fig 3.30. With change in core peak flux density. The harmonic components of the

secondary voltage waveform from sinusoidal supply can be seen in Fig. 3.31 the

harmonic existing in the primary current from the two peak flux densities excited

from PWM source can be seen in Fig 3.32. The harmonic from the secondary PWM

voltage waveform can be seen in Fig 3.33



76

Fig. ‎3-30 Harmonic content of sinusoidal primary current at peak flux densities of 0.4T and

1.0T

Fig. ‎3-31 Harmonic content of sinusoidal secondary voltage at peak flux densities of 0.4T and

1.0T

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1st 2nd 3rd 4th 5th 6th 7th 8th 9th

Av

era

ge

curr

ent

(Am

ps)

Harmonic order

0.4T

1.0T

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Av

era

ge

vo

lta

ge

(Vo

lts)

Harmonic order

0.4T

1.0T



77

Fig. ‎3-32 Harmonic content of PWM primary current at peak flux densities of 0.4T and 1.0T

Fig. ‎3-33 Harmonic content of PWM secondary voltage at peak flux densities of 0.4T and 1.0T

0

0.2

0.4

0.6

0.8

1

1.2

1.4


Av

era

ge

curr

ent

(Am

ps)

Harmonic order

0.4T

1.0T

0

5

10

15

20

25


Av

era

ge

vo

lta

ge

(Vo

lts)

Harmonic order

0.4T

1.0T



78

CHAPTER 4

4. Experimental apparatus and measuring technique

The apparatus comprised a 100 kVA, three-phase transformer core with associated

instrumentation to measure flux density, power loss and localised mechanical stress

within the core.

Core geometry 4.1.1

In order to investigate the core losses and mechanical stress under sinusoidal and

PWM excitations, experiments were carried out on high permeability grain oriented

(HGO) [51], three-phase 100 kVA transformer core. The core was built with single

step lap configuration with lamination of 100 mm wide, 0.3 mm thick and density of

7650 kg/m3. Overlap shift of 3 mm, the core has been used with three laminations per

stacking layer having [011] [100] texture, these are known as Goss texture. The

laminations are coated with insulating materials on both sides to provide good

electrical insolation and improve the texture of the material. Fig 4-1a, 4.1b and 4.1c

show the overall dimensions of the core [40].



79

(a)

(b)

(c)

Fig. ‎4-1 (a) Dimension of the middle limb. (b) Dimensions of the outer limb (c) Dimensions of the

yoke



80

Type of joints 4.1.2

The popular 045 - 090 joint was employed at the T-section and the 450 mitred overlap

joints were used at the corners.

Support and clamping 4.1.3

The core was built carefully to avoid air gaps in the joints. It was placed horizontally

on stiff wooden table. Fig. 4-2 shows each limb and yoke of the core has two holes

and two circular slots. The diameter of the holes was 1 cm and slot length was 1.1cm.

Transformer was then clamped by three wooden clamps in the limb 37cm × 3 cm

and two wooden clamps in the yoke with four holes 65cm ×5cm. Wooden clamp was

place over and underneath limb and yokes to avoid any bending. Fibre reinforced

plastic bolts inserted through the slot. Torque wrench was used to apply desired

clamp force onto the core.

Fig. ‎4-2 Three-phase transformer core



81

The photograph of the apparatus shown in Fig. 4-3 was used to magnetize the core,

transformer was energised under sinusoidal waveform and PWM waveform.

When the core was fed by three-phase sinusoidal supply voltage was stepped down

through three cascaded variacs. Three variacs, were used to give desired peak flux

density and to balance the secondary induced voltage.

Additional fine control adjustment was achieved by power analyser. Three primary

and secondary windings were connected to a precision digital power analyser

“NORMA D6000 Wide-Band Power Analyser System”. Digital oscilloscope was

used to record secondary induced voltage.

However, under PWM voltage excitation primary winding was connected to the

output of the inverter and the output voltage of the inverter was adjusted through the

front panel of the inverter. Transformer winding has 50 turns of PVC coated copper

wire with voltage rating of 600 V and 2.5 mm2 cross-sectional area. The windings

were connected in star configuration.

Under sinusoidal and PWM voltage excitation each limb of the core energised to

peak flux density of 0.4T, 0.6T and 1T, under load and no-load conditions.



82

Fig. ‎4-3 Photograph of magnetising and associated measurement system



83

4.2 Localised flux density calculation

In order to measure localised flux density within the transformer core, array of search

coils were wound on individual laminations as shown in Fig 4.9 to Fig 4.14. Single

turn search coils were placed in the rolling and in the transverse directions (RD and

TD) to detect the instantaneous flux density component at any instant of time in any

direction. The output of the search coil is connect to the DAQ card by means of

twisted search coils leads and then the output signal from the DAQ card is connected

to the Lab-View programme as shown in fig 4-8. Each detected signal has its

magnitude and angle with respect to the reference direction.

Equations (4.1) and (4.2) express the instantaneous induced voltages in the localised

search coil in the rolling and transverse directions.

dt

tt

dBAe

t

tt

)()( (4.1)

dt

tt

dBAe

r

rr

)()( (4.2)

Where and are the induced voltage in the rolling and transverse directions

respectively, and are the flux density in the rolling and transverse directions

respectively. and are cross-sectional area in the rolling and transverse

directions respectively. The instantaneous component of flux density can be obtained

by integrating equations (4.1) and (4.2)

The magnitude of the induced flux density )(tB , vectored sum of the )(tBtand

)(tBr at any instant in time, can be found as.

2/122 )()()( tBtBtB tr (4.3)

This equation can be used to calculate the instantaneous component of the localised

flux density under sinusoidal and PWM waveform [52].



84

Localised flux density measurement 4.2.1

Transformer core was energised by three-phase PWM inverter and by three-phase

sinusoidal supply. Measurements were taken separately for each condition.

Search coil technique was used to measure a peak value of localised flux density

passing through a given cross-sectional area. In order to obtain the most accurate

result out of the measurement, the area should not be very small because small cross

sectional area results in very low induced voltage [53], which can be effected by

noise and cause a distortion in the induced voltage waveform. In order to avoid any

distortion in the induced voltage waveform, the size of a cross-sectional area was

chosen as 1 cm on both rolling (RD) and transvers (TD) directions. Fig. 4-7 to Fig 4-

12.

In order to precisely locate the search coil upon test laminations, all the positions of

the locations were marked on the tested lamination. 0.3 mm holes were drilled using

drill “Dremel Model 850”. Polyester-coated 0.3mm wire was threated through the

holes and then each search coil leads were twisted tightly. Both sides of drilled holes

were insulated using a thin layer of spray varnish in order to protect the insulation of

the search coil wires and avoid short circuits between the lamination and the coil. At

each stage of search coil construction, a test was carried out using ohmmeter to check

for wire breakage or short circuit between the lamination and the search coil.



85

Construction and positioning of search coils 4.2.2

For the measurement of localised flux densities, single-turn search coils were

constructed by threading 0.3mm diameter enamelled copper wire through holes in

the laminations. The holes were 0.3mm in diameter, were accurately located and

drilled very slowly to avoid any localised stresses building up around the holes. The

holes were lightly countersunk on both sides of the lamination to avoid any damage

to the enamel coated wire. The test laminations were placed in large 3-zone Retort

furnace and then heat up to 8000C to relief stress induced in the lamination during

drilling process. After threading the search coils through the holes each pair of search

coil leads were twisted tightly together to avoid pick-up of any stray flux.

A large number of search coils were placed in the laminations located in the middle

of the core to obtain comprehensive localised flux measurements [54]. Another set of

search coils (reference coils) were wound around the limbs and yokes of the core.

These search coils were used to measure overall flux density.

Calibration and testing of search coils 4.2.3

Calibration of the localised search coils was carried out by measuring accurately

their lengths. A sample from each area under investigation was picked up at random.

The maximum variation in length was found to be 5%. The deviation of the

search coil axes from the rolling and transverse directions were marked with a tape.

All localised search coils were tested for continuity, insulation and connection. The

insulation of the search coil was determined when the core was in demagnetized state

by multimeter leads. The detected voltage of the multimeter recorded as reference to

ensure that the ends of the search coil are working in the right order. However,

induced generated signal in the search coil was measured by lab view.



86

Measurement preparation 4.2.1

The most two common techniques for measuring flux density is search coil

technique and needle probe technique. The method employed to measure localised

flux density in this work was search coil technique which was first discovered by

Brailsford and Mazza and others [31].

To measure the localised flux density, holes were drilled in the middle of the

laminations and near to the corner and T-joint where the flux changes its direction.

Single-turn search coils were wound to record dB/dt in the tested areas [42]. Core

was build and then single-turn search coil was wound around the yoke and limb to

measure overall flux density distribution. Fig. 4-3.

The output voltages from each search and reference coils were fed to the “Fluke

8050A Digital Multimeter” where their values were compared with labview

signals. The latter were fed to the DAQ card type module “NI USB” with a sampling

rate of 250 kS/s and then to the personal computer where measurements were taken.

Localised flux density distribution was measured by means of winding an array of

single-turn search coils on individual laminations. Localised flux densities were

measured in both RD-directions and TD directions. Therefore, search coils were

wound at right angles to each other at each point.

The magnitude and relative phase, in time, of voltage induced in the search coils

were measured and from these, the magnitude and direction of the flux density

vectors in space at individual points were determined. The magnitude and the

direction of the overall flux density at each test point of the lamination at any instant

in time were calculated by means of the formula:

= √

[53] (4.4)

Where is the localised flux vector in the rolling direction and is the flux vector

in transverse direction. The induced voltages in the search coils were measured using

following system illustrated in Fig. 4-4.



87

Fig. ‎4-4 Block diagram of virtual instrument for calculating magnetic flux density



88

4.3 Measurement results of localised power loss

Investigation on the localised power loss has been carried out when the core

energised by sinusoidal and PWM voltage excitation. Measurements were taken

under load and no-load conditions. Localised power loss measurements were taken at

peak flux density of 0.4T, 0.6T and 1.0T so comparison between localised power loss

under sinusoidal and PWM voltage excitation can be made. Equation 4.4 was used to

obtain localised power loss measurement.

During the measurement process, the overall accuracy of localised power loss was

affected by several parameters such as calculating the cross-sectional area of search

coils and data acquisition process was found with the accuracy of ± 1 of full scale

voltage. All localised power loss under sinusoidal and PWM voltage excitation was

measured at 50 Hz magnetising frequency. Table 4.1 to table 4.24 shows localised

power loss measurement under sinusoidal and PWM voltage excitation under load

and no-load conditions.



89

Table 4-1 Measurements of the localised power loss (W/kg) in the outer limb under sinusoidal

voltage excitation no-load condition with various peak flux densities

Core

excitation

(T)

Localised power loss (W/kg) at different positions

Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.33 0.26 0.26 0.23 0.26 0.36 0.37

0.6 0.38 0.36 0.32 0.27 0.30 0.38 0.43

1.0 0.65 0.65 0.64 0.55 0.59 0.66 0.66

Table 4-2 Measurements of the localised power loss (W/kg) in the outer limb under sinusoidal

voltage excitation load condition with various peak flux densities

Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.37 0.35 0.31 0.31 0.31 0.39 0.39

0.6 0.47 0.46 0.45 0.40 0.41 0.59 0.59

1.0 0.71 0.72 0.68 0.69 0.68 0.76 0.77



90

Table 4-3 Measurements of the localised power loss (W/kg) in the outer limb under PWM


Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.41 0.35 0.33 0.29 0.31 0.39 0.42

0.6 0.46 0.43 0.41 0.35 0.37 0.44 0.53

1.0 0.71 0.69 0.63 0.62 0.63 0.71 0.72

Table 4-4 Measurements of the localised power loss (W/kg) in the outer limb under PWM


Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0. 45 0.43 0.43 0.37 0.35 0.45 0.46

0.6 0.59 0.56 0.51 0.48 0.53 0.59 0.61

1.0 0.83 0.75 0.79 0.71 0.73 0.82 0.85



91

Fig. ‎4-5 Locations of localised search coils in the outer limb



92

Table 4-5 Measurements of the localised power loss (W/kg) in the corner joint under sinusoidal


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions

Localised power loss at different excitation (W/kg)

1 0.73 0.86 1.94

2 0.56 0.86 1.26

6 0.43 0.48 0.79

9 0.68 0.85 1.55

10 0.43 0.66 0.86

15 0.53 0.84 1.15

Table 4-6 Measurements of the localised power loss (W/kg) in the corner joint under sinusoidal


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.79 1.87 2.77

2 0.75 1.56 2.39

6 0.48 0.95 1.11

9 0.77 1.69 2.56

10 0.69 1.13 1.28

15 0.71 1.51 2.16



93

Table 4-7 Measurements of the localised power loss (W/kg) in the corner joint under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.93 2.74 3.97

2 0.79 2.69 3.93

6 0.58 1.47 2.16

9 0.86 2.69 3.93

10 0.68 1.50 3.81

15 0.75 1.97 3.85

Table 4-8 Measurements of the localised power loss (W/kg) in the corner joint under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.97 3.77 5.76

2 0.85 3.49 4.36

6 0.63 1.66 3.81

9 0.98 3.67 5.43

10 0.79 2.61 4.07

15 0.86 2.67 4.16



94

Fig. ‎4-6 Locations of the search coils in the outer limb corner joint, rolling (R) and transvers

Directions (T)



95

Table 4-9 Measurements of the localised power loss (W/kg) in the corner yoke joint under

sinusoidal voltage excitation no-load condition with various peak flux densities

Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.58 0.74 1.87

2 0.50 0.65 0.81

6 0.58 0.71 1.38

9 0.43 0.57 0.72

10 0.54 0.67 0.92

15 0.57 0.68 1.21


sinusoidal voltage excitation load condition with various peak flux densities

Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.65 1.52 1.82

2 0.44 0.93 1.26

6 0.57 1.51 1.59

9 0.34 0.84 1.09

10 0.56 1.13 1.33

15 0.57 1.19 1.33



96

Table 4-11 Measurements of the localised power loss (W/kg) in the corner yoke under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.68 1.86 3.17

2 0.54 1.12 2.29

6 0.65 1.77 2.98

9 0.44 0.93 2.11

10 0.65 1.32 2.83

15 0.64 1.67 2.98


PWM voltage excitation load condition with various peak flux densities

Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.78 2.68 3.93

2 0.64 1.79 2.30

6 0.75 2.19 3.15

9 0.63 1.17 2.13

10 0.65 1.82 2.47

15 0.67 1.93 2.58



97

Fig. ‎4-7 Locations of the search coils in the outer yoke corner joint, rolling (RD) and transfer

directions (TD)



98

Table 4-13 Measurements of the localised power loss (W/kg) in the middle limb under sinusoidal


Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.43 0.38 0.38 0.33 0.36 0.37 0.43

0.6 0.53 0.41 0.41 0.36 0.38 0.38 0.45

1.0 0.82 0.82 0.76 0.71 0.71 0.76 0.82

Table 4-14 Measurements of the localised power loss (W/kg) in the middle limb under sinusoidal


Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.46 0.39 0.38 0.35 0.36 0.36 0.43

0.6 0.63 0.45 0.47 0.42 0.42 0.45 0.45

1.0 0.92 0.87 0.87 0.80 0.82 0.86 0.89



99

Table 4-15 Measurements of the localised power loss (W/kg) in the middle limb under PWM


Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.49 0.46 0.46 0.38 0.41 0.53 0.56

0.6 0.61 0.56 0.59 0.47 0.48 0.74 0.79

1.0 0.89 0.80 0.87 0.86 0.80 0.85 0.90

Table 4-16 Measurements of the localised power loss (W/kg) in the middle limb under PWM


Core

excitation

(T)


Position

1

Position

2

Position

3

Position

8

Position

11

Position

12

Position

13

0.4 0.56 0.77 0.56 0.57 0.53 0.82 0.72

0.6 0.73 0.86 0.77 0.76 0.67 0.97 0.95

1.0 1.04 1.04 0.97 0.95 0.95 1.08 1.06



100

Fig. ‎4-8 Locations of the search coils in the middle limb



101

Table 4-17 Measurements of the localised power loss (W/kg) in the yoke T-joint under

sinusoidal voltage excitation no-load condition with various peak flux densities

Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.46 0. 69 0.92

3 0.37 0.52 0.73

5 0.42 0.63 0.80

8 0.45 0.65 0.84

10 0.41 0.57 0.70

13 0.42 0.59 0.75

16 0.33 0.53 0.70

Table 4-18 Measurements of the localised power loss (W/kg) in the yoke T-joint under

sinusoidal voltage excitation load condition with various peak flux densities

Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.46 0.74 1.30

3 0.39 0.56 0.75

5 0.45 0.68 1.00

8 0.45 0.66 1.17

10 0.43 0.66 0.76

13 0.42 0.64 0.85

16 0.36 0.58 0.73



102

Table 4-19 Measurements of the localised power loss (W/kg) in the yoke T-joint under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.63 0.91 1.38

3 0.44 0.76 1.14

5 0.54 0.80 1.25

8 0.63 0.87 1.35

10 0.47 0.85 1.17

13 0.45 0.83 1.30

16 0.45 0.74 1.10

Table 4-20 Measurements of the localised power loss (W/kg) in the yoke T-joint under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.69 1.73 2.90

3 0.49 0.87 1.97

5 0.62 1.26 2.25

8 0.68 1.65 2.30

10 0.48 1.29 2.17

13 0.53 1.23 1.96

16 0.47 0.83 1.19



103

Fig. ‎4-9 Locations and direction of the search coils in the T-joint



104

Table 4-21 Measurements of the localised power loss (W/kg) in the limb T-joint under sinusoidal


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.48 0.87 0.96

3 0.42 0.77 0.96

5 0.35 0.58 0.84

8 0.37 0.63 0.83

10 0.39 0.72 0.84

13 0.50 0.87 0.99

14 0.41 0.74 0.89

Table 4-22 Measurements of the localised power loss (W/kg) in the limb T-joint under sinusoidal


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.67 1.31 1.71

3 0.58 0.90 1.64

5 0.35 0.67 1.02

8 0.36 0.73 1.22

10 0.53 0.88 1.61

13 0.67 1.36 1.96

14 0.53 0.88 1.35



105

Table 4-23 Measurements of the localised power loss (W/kg) in the limb T-joint under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.68 1.83 2.41

3 0.62 1.76 2.22

5 0.54 1.10 1.24

8 0.54 1.22 1.35

10 0.55 1.41 1.90

13 0.80 1.98 2.73

14 0.56 1.57 1.98

Table 4-24 Measurements of the localised power loss (W/kg) in the limb T-joint under PWM


Core excitation

(T)

0.4 0.6 1.0

Search coil

positions


1 0.76 1.83 2.69

3 0.75 1.79 2.61

5 0.54 1.13 1.94

8 0.54 1.40 2.19

10 0.64 1.57 2.59

13 0.86 1.98 2.82

14 0.68 1.74 2.30



106

Fig. ‎4-10 Locations and directions of the search coils in the T-joint R and T directions



107


Localised power losses were obtained under sinusoidal and PWM voltage

waveforms, Tables 4.1, 4.2, 4.3 and 4.4. Show measurements of the localised power

loss in the middle of the outer limb. As shown in Fig. 4-5, results were obtained from

15 regions at different peak flux densities of 0.4T, 0.6T and 1.0T. Measurement

under load condition shows higher localised power loss than that under no-load

condition, under both sinusoidal and PWM waveforms. Results have shown that

more localised power loss flow in the middle of the limb than that close to the edge.

At the corner limb joints as the flux flow in two directions, search coils were placed

in two orthogonal axes, which are known as rolling and transvers directions (RD)

and (TD). Fig. 4-6. At all magnetisation, peak flux density result was obtained from

15 regions. Tables 4.5, 4.6, 4.7 and 4.8 show the magnitude of the localised power

loss was higher under load condition. It can be seen that search coils close to cutting

edges have shown higher localised power loss than search coils away from the

cutting edge.

At yoke corner joints Fig. 4-7, shows localised power loss in 15 regions the

magnitude of the localised power loss was obtained in tables 4.9, 4.10, 4.11 and 4.12

which have shown higher localised power loss near the cutting edge as the flux

jumps to the next layer. This is because large flux flows in both RD and TD

directions changing its direction from limb to yoke.

At the central limb Fig. 5-8, shows localised power loss in 15 regions tables 4.13,

4.14, 4.15, and 4.16 at all magnetising peak flux densities all 15 search coils have

reached their saturation value.

At the T-joint yoke joint Fig. 4-9, tables 4.17, 4.18, 4.19 and 4.20 show localised

power losses in 16 regions, when the core is energised under sinusoidal and PWM

loads and no-load conditions, all 16 regions have reach their saturation value.

At the T-joint limb joint Fig 4-10, tables 4.21, 4.22, 4.23 and 4.24 have shown

localised power loss in 14 regions. The results have shown higher power loss near

the joints which are close to the cutting edges than that away from the cutting edges.

This shows that there is more flux concentration in these regions and the magnitude



108

of the resultant flux density under both sinusoidal and PWM excitations are varied.

More details about the results obtained are discussed in 5.5 analysis and discussion.

Localised power loss obtained in the outer limb of the model three-phase 4.3.2

transformer core with various peak flux densities

The efficient operation of power transformer core depends to a large extent on the

design of the joints between their limbs and yokes. In the three-phase, three-limb

core, the most complex joints are the T-joints. At the intersection of the centre limb

and yokes the joint should be constructed to give mechanical stability to the core and

to be magnetically efficient. Table 4-1 to table 4-24 show localised power loss under

sinusoidal and PWM voltage excitations. Transformer core was energised under

sinusoidal and PWM voltage excitations at 50 Hz frequency. In order to study the

localised power losses occurred in transformer core under sinusoidal and PWM

waveforms, equal level of the peak flux density was applied to the core at 0.4 T, 0.6

T and 1.0 T. Localised Measurements were taken in the limbs, yoke, corner and T-

joint of the transformer core.

As the flux flows in one direction in the middle of the lamination, search coils

embedded on a test lamination in the rolling direction to record localised flux passing

through the selected areas as shown in Fig. 4-5. During measurements of localised

loss under sinusoidal and PWM voltage excitation, the average value of localised

power loss was found to be almost the same under both load and no-load conditions.

Firstly, when the core was energised under sinusoidal waveform at peak flux density

of 0.4T under load and no-load conditions, tables 4-1 and 4-2 show the highest

localised power loss was recorded to be in search coil positions 13, 12 and 1. And the

smallest was found to be in search coil positions 3, 11 and 8. So localised search coil

position 13 has shown the largest value of localised power loss under load and no-

load conditions. Moreover, smallest values of localised power losses were varied to

be at different search coil positions.

Same result was obtained when the core was energised at peak flux density of 0.4 T

under PWM voltage excitation, under load and no-load conditions, tables 4-3 and 4-



109

4. Highest localised power loss value was found to be in search coil positions 13,

nevertheless smallest value was found to be varied between search coils 3, 11 and 8.

Comparing the result obtained during the measurement process under sinusoidal and

PWM voltage excitations under load and no-load conditions, tables 4-1, 4-2, 4-3 and

4-4, agreement of the result was obtained in search coil position 13 which has shown

the highest value of localised power loss. Comparing the result obtained when the

core was energised under sinusoidal and PWM voltage excitations, at peak flux

density of 0.4 T under load condition under PWM voltage excitation all search coil

have shown larger value of localised power loss nevertheless some search coils have

not reached their saturation value under both excitation conditions.

Increasing the energising flux density to 0.6T, under sinusoidal waveform load and

no-load conditions, the highest localised power loss values were found to be in

search coil positions 13, 12 and 1, and the smallest value of localised power losses

were found to be in search coils positions 3, 11 and 8.

When transformer core energised with PWM voltage excitation at 0.6T under load

and no-load conditions, search coils positions 13, 12 and 1 have recorded the highest

value of localised power loss. And the rest of the search coils have recorded almost

same value of localised power loss.

Comparing the result obtained at 0.6T under PWM with the result obtained under

sinusoidal voltage excitation under load and no-load conditions, agreement of the

result was obtained in search coil position 13 which have shown the highest value of

localised power loss under both energising conditions.

Increasing the energising flux to 1.0T, under sinusoidal waveform load condition,

search coil positions 13, 12, and 1 recorded the highest value of localised power loss,

whereas search coil positions 3, 11 and 8 have shown the lowest value of localised

power loss. However, when the core energised under no-load condition all 15 search

coils have shown almost a same values of localised power loss distribution.

When the core energised by PWM voltage excitation at peak flux density 1.0 T under

no-load condition search coil positions 13, 12 and 1 have shown the highest value of

localised power loss but they have not reach their saturation value. Whereas, the rest



110

of the search coils have shown almost a same value. However, energising the core

under load condition search coil positions 13, 12, and 1 have shown the highest value

of localised power loss, whereas search coil positions 3, 11 and 8 have shown the

lowest value of localised power loss.

Comparing the result obtained under PWM with the result obtained under sinusoidal

voltage excitation under load conditions. The highest value of localised power losses

was agreed to be find in search coil positions 13 and 12. Moreover, the smallest

value of localised power loss was varied. Energising the core under no-load

condition, largest and smallest value of localised power losses were agreed to be in

positions 13 and 12. Fig. 4-11 shows the variation of localised power loss under

sinusoidal and PWM voltage excitations under no-load condition, And Fig. 4-12.

shows the variation of localised power loss under sinusoidal and PWM voltage

excitations under load condition. Both measurements were taken at 50 Hz. Highest

values of tables 4-1, 4-2, 4-3. And 4-4 were chosen as reference.



111

Fig. ‎4-11 Comparison of localised power loss under sinusoidal and PWM voltage excitations

(No-load condition) at the center of the outer limb at various peak flux densities (T), 50 Hz.

Fig. ‎4-12 Comparison of localised power loss under sinusoidal and PWM voltage excitations

(Load condition) at the center of the outer limb at various peak flux densities (T), 50 Hz.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)

Variation of the peak flux density (T)

SIN

PWM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



112

From Fig. 4-11, 4-12, it could concluded that localised power losses when the core

was energised under sinusoidal and PWM waveforms under no-load condition at

peak flux densities of 0.4T and 0.6T have increased under PWM excitation by factors

of 11%, and 18% respectively. However, when the core was energised under load

condition, localised power losses have increased under PWM excitation by factors of

15% and 3% respectively, Increasing the energising induction to 1.0T, localised

power loss under PWM voltage excitation has increased under no-load condition by

a factor of 8%, whereas when the core was energised under load condition localised

power loss has increased under PWM waveform by a factor of 9%.

Localised power loss obtained in the middle limb of the model three-4.3.3

phase transformer with various peak flux densities

In order to study the localised distribution of power loss in central limb of three-

phase transformer core, search coils were positioned in the centre of the lamination

in the rolling direction (RD), where the flux is mainly flowing in the rolling

direction. Fig. 4-8 shows the positions of localised search coils and tables 4-13, 4-14,

4-15 and 4-16 show the magnitude of localised power losses in the central limb of

three-phase transformer.

Energising the core under sinusoidal voltage excitation under no-load and load

conditions at peak flux density 0.4T, search coil positions 1 and 13 have reached

their saturation value, whereas. When the core was energised at peak flux density of

0.4T under PWM wave excitation under no-load and load conditions, all 15 search

coils have reached their saturation value and recorded the highest localised power

loss.

Comparing the results obtained under PWM voltage excitation with the results

obtained under sinusoidal voltage excitation under no-load conditions at peak flux

density of 0.4T, the highest value of localised power loss was recorded in search coil

position 1 and it was 6% higher under PWM voltage excitation. Whereas, when the

core energised under load condition the variation of localised power loss had a value

of 21 % higher under PWM waveform.



113

Increasing the energising flux density to 0.6T under sinusoidal and PWM waveforms

under no-load and load conditions, again same results were obtained. Search coils

position 1 and 13 have shown the highest values of localised power loss.

Comparing the results obtained under PWM with the result obtained under sinusoidal

voltage excitation at 0.6T, the highest value of localised power loss induced in search

coil position 1 and the smallest value was found to be in search coil position 8.

Comparing the results under no-load and load conditions, the variation of localised

power losses had values of 13% and 27% respectively, higher under PWM

waveform.

Comparing the results obtained under PWM with the results obtained under

sinusoidal at peak flux density of 1.0T, the highest value of localised power loss

occurred in search coil position 1 under load and no-load conditions. As a result of

comparison between PWM and sinusoidal waveforms it could be concluded that

under no-load and load conditions localised power loss had values of 7% and 3%

respectively higher under PWM waveform.

Fig. 4-13 shows the variation of localised power loss under sinusoidal and PWM

waveform excitations under no-load condition and Fig. 4-14, shows variation of

localised power loss under sinusoidal and PWM excitation under load condition at

50Hz. Highest values of localised power losses presented in tables 4-13, 4-14, 4-15.

and 4-16 were chosen as reference.



114

Fig. ‎4-13 Comparison of localised power loss under sinusoidal and PWM voltage excitation (No-

load condition) central limb at various peak flux densities (T), 50 Hz

Fig. ‎4-14 Comparison of localised power loss under sinusoidal and PWM voltage excitation

(Load condition) central limb at various peak flux densities (T), 50 Hz

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)

Variation of the peak flux densities (T)

SIN

PWM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



115

Comparison between localised power loss obtained in the middle of the 4.3.4

outer and central limbs of the model three-phase transformer core with various

peak flux densities

Search coils were positioned in fifteen and fourteen regions in the same locations in

the outer and central limbs as shown in Fig. 4-5 and 4-8 respectively. So comparison

between sinusoidal and PWM flux conditions at various peak flux density at same

position of the search coil can be made between central and outer limbs. Under

sinusoidal voltage excitation at 0.4T under no-load conditions, localised power losses

in the central limb were higher than those of the outer limb by the factor of 13%.

Furthermore, under load condition central limb represents higher values of localised

power loss than the outer limb by the factor of 16%. However, comparing the results

obtained in the outer and central limbs when the core was energised by PWM voltage

excitation under no-load and load conditions, central limb had shown higher

localised power losses by factors of 14% and16% respectively.

Comparing localised power loss when the core was energised at peak flux density of

0.6T under sinusoidal waveform under no-load and load conditions, central limb had

higher localised power loss than the outer limb by factors of 18% and 6%

respectively. Comparing the results obtained between outer at central limb when the

core was energised by PWM voltage excitation at 0.6T under no-load and load

conditions, central limb had shown higher value of localised power loss by the factor

of 13% and 29% respectively.

Comparing localised power loss between outer and central limbs when the core was

energised under peak flux density of 1.0T under sinusoidal no-load and load

conditions, central limb has higher magnitudes of localised power loss than those in

outer limb by 19% and 16% respectively. However, comparing the results obtained

when the core was energised under PWM waveform under no-load condition, central

limb had value of 19% higher than the outer limb whereas under load condition

central limb had a value of 7% higher than the outer limb.

During all comparison between outer and central limb under load and no-load

conditions, localised measurements were higher in the central limb than that in the



116

outer limb this due to the flux flowing in the central limb is higher than the flux

flowing in the outer limb and could be due to the grain-oriented size.

Localised power loss obtained in the limb corner joints of the model 4.3.5

three-phase transformer core with various peak flux densities

In order to investigate localised power loss in the joint areas, two search coils were

placed, one search coil placed on the rolling direction (RD) and another search coil

were placed on the transvers direction (TD). The reason why there were two search

coils was because flux changes it is direction and jumps from one lamination to the

next lamination. Moreover, rotational flux occurs at the joint areas. However, search

coil placed in the rolling direction was used to measure localised flux density in the

rolling direction and the search coil placed in the transverse direction was used to

measure localised flux density in the transvers direction. It was found that the flux in

the rolling direction is three or four times larger than that of flux travelling in the

transvers direction. The search coil holes were another factor on distribution the

localised measurements on the transformer core, so they must be as small as possible

in order to provide well balanced flux all over the areas. Large sized holes may cause

disturbance of the magnetic flux in those areas. Fig. 4-6, 4-7, 4.9 and 4-10 show

rolling and transvers directions of the search coils. Equation 4.8 was used to calculate

the average value of localised magnetic flux occurring in the selected positions.

Localised power loss was calculated at the corner joint Fig. 4-6. When the core was

energised at different peak flux densities of 0.4T, 0.6T and 1.0T, measurements

were again taken under sinusoidal and PWM voltage excitations under no-load and

load conditions. From tables 4-5, 4-6, 4-7 and 4-8, it can be seen that fifteen regions

were chosen to measure localised power loss in which they have reached their

saturation values at all energising peak levels. Furthermore, it can be seen that search

coils at positions 1, 2 and 9 which were placed very close to the cutting edge have

shown the highest value of localised power loss. This is because of high amount of

the flux circulating in those areas. However, further away from the cutting edges

localised power loss was found to be decreasing, search coil positions 6 and 10. This

could be because high amount of localised magnetic flux density were still in the

rolling direction.



117

Comparing localised power loss when the core was energised under PWM and

sinusoidal waveforms. At different peak flux density of 0.4T, 0.6T, and 1.0T under

load and no-load conditions, localised power losses were higher under PWM voltage

excitation. Fig 4.15 shows variation of localised distribution of power loss under

sinusoidal and PWM voltage excitations under no-load condition and fig. 4-16 shows

variation of localised power loss under sinusoidal and PWM voltage excitation under

load condition at 50Hz. Highest values presented on table 4-5, 4-6, 4-7 and 4-8 were

chosen as reference.


load condition) at limb corner joints at various peak flux densities (T), 50 Hz.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



118


(Load condition) at limb corner joints at various peak flux densities (T), 50 Hz.

Localised power loss obtained in the yoke corner joints of the model 4.3.6

three-phase transformer core with various peak flux densities

In order to compare localised power loss occurring at the limb and yoke on same

positions, search coils were placed on the yoke joint as shown in fig. 4-7.

Measurements were again taken under sinusoidal and PWM voltage excitations,

under load-and no-load conditions. Fifteen search coils were chosen randomly to

study localised power loss. Tables 4-9 and 4-10, show the values of localised power

loss distribution under sinusoidal waveform and tables 4-11, and 4-12 show the

magnitude of localised power losses under PWM waveform.

Firstly, measurements were taken under sinusoidal waveform at peak flux density

0.4T under no-load and load conditions, the average value of instantaneous localised

power loss at the corner yoke joint was found to be in search coil position 1.

Localised power loss was found to be decreasing away from the corner joint search

coil position 10. Localised power loss at right corner search coil position 15 was

compared with search coil position 1 near the cutting edge and it was found that

0

1

2

3

4

5

6

7

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



119

localised power loss was found to be decreased in right corner under no-load and

load conditions by factors of 1% and 14% respectively. However, when the core was

energised under PWM waveform at peak flux density 0.4T under no-load and load

conditions, search coils at all positions have reached their saturation value.

Nevertheless, search coil position 6 has recorded the lowest value of localised power

losses.

Highest magnitude value of localised power losses are shown in tables 4-9, 4-10, 4-

11 and 4-12, were chosen as reference to compare the results obtained under PWM

with the results obtained under sinusoidal voltage excitation. Comparing the results

obtained with the core energised at peak flux density of 0.4T, localised power loss

was found to be increased near the cutting edge joint and decreased further away

from the cutting-edge joint, search coil position 10. Moreover, localised power loss

was found to be higher with the core energised under PWM voltage excitation under

no-load and load conditions, by factors of 14% and 16% respectively.

Increasing the energising flux to 0.6T under sinusoidal waveform, no-load condition

highest magnitude value of loci power loss was recorded to be in search coil position

1, and lowest magnitude value of loci power loss was recorded to be in search coil

positions 6, 10 and 15. When the core was energised under load condition, highest

value of loci power loss was found to be in positions 1, 2 and 9 and the lowest value

of loci power loss was found to be in search coil position 6. Energising the core with

same peak flux density under PWM voltage excitation under no-load and load

conditions, all search coils have reached their saturation value and search coil

position 1 has shown the highest value of localised power loss.


sinusoidal voltage excitation at 0.6T, localised power loss was found to be increased

under PWM voltage excitation under no-load and load conditions by factors of 60%

and 43%, respectively higher than sinusoidal voltage excitation.

More comparisons were made with the core energised at peak flux density of 1.0T.

Firstly, measurements were taken under sinusoidal no-load and load conditions, the

highest magnitude value of localised power loss was found to be near coroner joint

and inside cuter edge joint search coil positions 1, 2 and 15. And the lowest



120

magnitude value of the localised power loss was found to be in search coil positions

6 and 10. Nevertheless, all search coils have reached their saturation value.

When the core was energised under PWM voltage excitation at peak flux density of

1.0T under no-load and load conditions, the highest magnitude value of localised

power loss was again found to be near coroner joint and inside cuter edge search coil

positions 1, 9 and 15. And the lowest magnitude value of localised power loss was

kept in search coil positions 6 and 10.


sinusoidal voltage excitation at peak flux density of 1.0T. Localised power loss was

found to be increased under PWM voltage excitation under no-load and load

conditions by factors of 41% and 53 %higher than sinusoidal voltage excitation.

Fig. 4-17, shows variation of localised power loss under sinusoidal and PWM

voltage excitations under no-load condition and Fig. 4-18, localised power loss under

sinusoidal and PWM voltage excitations under load condition at 50Hz. Highest

values presented on table 4-9, 4-10, 4-11 and 4-12 were chosen as reference.

Fig. ‎4-17 Comparison of localised power loss under sinusoidal and PWM voltage excitation (no-

load condition) at yoke corner joints at various peak flux densities (T), 50 Hz.

0

0.5

1

1.5

2

2.5

3

3.5

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



121


(Load condition) at various peak flux densities (T), 50 Hz.

Comparison between localised power loss obtained in the limb and yoke 4.3.7

corner joints of the model three-phase transformer core with various peak flux

densities

Highest magnitude values of localised power loss presented on tables 4-5, 4-6, 4-7,

4-8, 4-9, 4-10, 4-11 and 4-12 were analysed to study the difference of magnitude

value of localised power loss between the limb and the yoke. Comparing the results

obtained under sinusoidal waveform across the limb and yoke at the corner joints,

with the core energised at peak flux density of 0.4T under no-load and load

conditions, localised power loss was found to be higher in the limb than that of the

yoke by factors of 20% and 17% respectively. Furthermore, with the core energised

under PWM voltage excitation with the peak flux density of 0.4T under no-load

condition, localised power loss in the limb had a value of 26% higher than that in the

yoke, while under load condition localised distribution in the limb had a value of

19% higher than that in the yoke.

Comparing the results obtained under sinusoidal waveform between the limb and

yoke with the core energised at peak flux density of 0.6T under no-load and load

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



122

conditions, localised power losses were found to be 13% and 18% respectively

higher in the limb than those of the yoke. However, comparing the result obtained

between the limb and yoke when the core energised under PWM voltage excitation

with the peak flux density of 0.6T under no-load and load conditions, localised

power losses in the limb had values of 32% and 28% higher than those in the yoke,

Increasing the energising flux to 1.0T hence more comparisons between localised

power loss occurred in the limb and in the yoke had been obtained. By comparing the

results obtained when the core was energised under sinusoidal waveform under no-

load and load conditions, localised power losses were found to be 3% and 34%

higher in the limb than those of the yoke. However, comparing the results obtained

between the limb and yoke when the core energised under PWM voltage excitation

with the peak flux density of 1.0T under no-load and load conditions, localised

power losses in the limb had values of 20% and 31% higher than those in the yoke.

It could be concluded that localised power loss was higher in the limb than that of the

yoke. This was due to the flux density inside the yoke being less than that in the limb

at all magnetising levels under no-load and load conditions.

Localised power loss obtained in the yoke- 045 joints with various peak 4.3.8

flux densities

Fifteen localised search coils were mounted on the yoke- 045 at the T-joint as shown

in fig. 4-9. Localised power loss was measured as shown in tables 4-17, 4-18, 4-19

and 4-20. Firstly, measurements were taken at peak flux density of 0.4T under

sinusoidal and PWM waveforms under no-load and load conditions, search coil

positions 1, 5 and 8 show the highest value of localised power loss, whereas search

coil positions 3, 10 and 16 have shown the lowest magnitude value of loci power

loss.

Same results were obtained when the core energised at 0.6T under sinusoidal and

PWM waveforms under load and no-load conditions. Search coil positions 1 and 8

have kept the highest value of localised power loss.



123

Further increasing of the energised flux density to 1.0 T under sinusoidal and PWM

waveforms under load and no-load conditions give same result obtained from search

coil positions 1 and 8 as they kept the highest magnitude values of localised power

loss while search coil position 3 and 16 show the lowest magnitude values of

localised power loss.

Comparing the results obtained in search coil position 1 at the top of the left corner

with result obtained by search coil position 13 at the top right corner, search coil

position 1 has shown the highest value of localised power loss under both sinusoidal

and PWM waveforms. Further comparisons have been obtained away from the

cutting edges, search coil position 3 was compared with the search coil position 16

under all levels of the magnetising peak flux density. Search coil position 3 has

shown highest value of localised power loss under sinusoidal and PWM voltage

excitations. This could be due to the size of the grain boundary.


voltage excitations under no-load condition, and Fig 4-20, has shown the variation of

localised power loss under sinusoidal and PWM voltage excitations under load

condition at 50Hz. Highest values presented on table 4-17, 4-18, 4-19 and 4-20 were

chosen as reference.



124

Fig. ‎4-19 Comparison of localised distribution of power loss under sinusoidal and PWM voltage

excitation (No-load condition) at various peak flux densities (T), 50 Hz


(Load condition) at various peak flux densities (T), 50 Hz

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM

0

0.5

1

1.5

2

2.5

3

3.5

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)


SIN

PWM



125

The average value of localised power loss under sinusoidal waveform in the yoke-

045 T-joint, Fig 4-9, was recorded to be increased near the joint, for instance at 0.4T

under no-load and load conditions. Search coil position 1 and search coil position 3

were compared. The magnitude of localised power loss was increased by the factor

of 19% and 15% respectively in search coil position 1. More comparisons have been

obtained between the positions of the search coil at 0.6T under no-load and load

conditions, the magnitude of localised power loss at search coil position 13 at the

right top corner near the edge was compared with search coil position 8. The average

value of the localised power loss was 9% and 3% higher in search coil position 8.

Further comparisons have been obtained at core peak flux density 1.0T under no-load

and load conditions, comparing top left corner search coil position 1 with the top left

corner search coil position 13, the magnitude of localised power loss in search coil

position 1 under no-load and load conditions had a value of 18% and of 34% higher

than search coil position 13.

More comparisons of the results have been made, with the core energised under

PWM voltage excitation, same search coil positions were compared. For example,

under no-load condition at 0.4T the average value of localised power loss in search

coil position 1 was 30% higher than search coil position 3. While under load

condition it was again higher in search coil position 1 by a factor of 28%. However,

with the core energised at 0.6T search coil positions 13 was compared with search

coil position 8 under no-load and load conditions. The magnitude of localised power

loss was higher in position 8 by factors of 4% and 25% respectively. Increasing the

energising flux to 1.0T search coil position 1 was compared with search coil position

13 under no-load and load conditions. The magnitude of localised power losses were

higher in search coil position 1 at the left top corner by factors of 5% and 32%

respectably.



126

Localised power loss obtained in the limb T joints with various peak flux 4.3.9

densities

At limb T-joint, 14 search coils were chosen to study localised power loss as shown

in fig 4-10, and tables 4-21, 4-22, 4-23 and 4-24 show the variation of localised

power loss against time under sinusoidal and PWM waveforms under load and no-

load conditions. With the core energised under sinusoidal waveform at peak flux

density of 0.4T under no-load and load conditions, search coil positions 13 and 1

have shown the highest value of localised power loss. Away from the cutting joint

search coil positions 6 and 7 have shown the lowest value of localised power loss.

However, comparing search coil position 5 with search coil position 8 under no-load

and load conditions, localised power loss had a value of 5% and 2% respectively

higher in search coil position 8.

Increasing the energised flux to 0.6T, search coil position 13 has shown the highest

magnitude value of localised power loss. Whereas, search coil position 5 has shown

the lowest value of localised power loss. Comparing the variation of localised power

loss under no-load and load conditions, between the highest and lowest value

induced in the search coil position 13 and search coil position 5, the results obtained

had shown that under no-load condition search coil position 5 had a value of 33%

higher localised power loss than search coil position 5, while under load condition it

was 50% higher in search coil position 13.

Increasing the energised flux to 1.0T when measurements were taken under no- load

condition, search coil positions 13, 1 and 16 have shown the highest value of

localised power loss, and search coil position 8 has shown the lowest value of

localised power loss. Comparing the result has been obtained between the highest

and lowest induced power loss distribution under no-load and load conditions, so

hence localised power loss in search coil position 13 was compared with localised

power loss in search coil position 8. Localised power loss in search coil position 13

had a value of 16% and 37% respectively, higher than the localised power loss in

search coil position 8.

When the core was energised at peak flux densities of 0.4T, 0.6T and 1.0T, under

PWM voltage excitation under no-load and load conditions, same result of highest



127

and lowest induced localised power loss was obtained at the same position of the

search coils as those have been obtained under sinusoidal voltage excitation. At all

magnetising peak value search coil position 13 kept the highest value of localised

power loss. And search coil position 8 kept the lowest value of localised power loss.

Comparing the result between the highest and lowest localised power loss, under no-

load condition at 0.4T, 0.6T and 1.0T, search coil position 9 had values of 32%, 38%

and 50% respectively, higher than search coil position 13. While under load

condition at magnetising flux of 0.4T, 0.6T and 1.0T, localised power loss of search

coil position 13 was higher than the localised power loss in search coil position 8 by

37%, 41% and 28% respectively.

Comparing the highest value of localised power loss under sinusoidal and PWM

voltage excitation at peak flux density 0.4T under no-load condition, the highest

value of localised power loss was recorded at search coil position 13 which has a

value of 37% higher under PWM voltage excitation, However, with the core

energised under load condition, localised power loss was 22% higher under PWM

voltage excitation. Further comparing of the highest result of localised power loss

detected by the search coils has been obtained with the core energised under

sinusoidal and PWM waveforms at peak flux density of 0.6T under no-load

condition, localised power loss had a value of 56% higher under PWM waveform,

whereas under load condition it was higher by factors of 31% under PWM voltage

excitation. However, more comparing of localised power loss has been obtained with

the core energised under PWM and sinusoidal waveforms. Increasing the energising

flux to 1.0T the highest localised power loss under PWM waveform was compared

with the highest value of localised power loss with the core energised under

sinusoidal waveform. Under no-load and load conditions localised power loss had a

value of 63% and 30% respectively higher under PWM voltage excitation.

It can be concluded that localised power loss was higher under PWM voltage

excitation in the T-joint (limb-joint) under all levels of magnetising peak flux density

under load and no-load conditions.


voltage excitation under no-load condition, and Fig. 4-22, shows the variation of



128

localised power loss under sinusoidal and PWM voltage excitation under load

condition at 50Hz. Highest variation values presented on tables 4-21, 4-22, 4-23 and

4-24 were chosen as reference.


load condition) at limb T-joints at various peak flux densities (T), 50 Hz.


(Load condition) at limb T-joints at various peak flux densities (T), 50 Hz.

0

0.5

1

1.5

2

2.5

3

0.4T 0.6T 1.0T

Po

wer

lo

ss (

W/k

g)

Variation of the peak flux densities

SIN

PWM

0

0.5

1

1.5

2

2.5

3

0.4T 0.6T 1.0T

Po

we

r lo

ss (

W/k

g)

Variation of the peak flux densities

SIN

PWM



129

Comparison between power loss obtained in the limb and yoke T joints 4.3.10

with various peak flux densities

Comparing localised power loss obtained in the T-joint and yoke- 045 joint under

sinusoidal waveform at peak flux density of 0.4T under no-load condition. Search

coil position 13 in the limb T-joint. Fig. 4-10, was compared with the search coil

position 8 in the yoke- 045 joint, Fig. 4-9. Magnitude of comparisons value occurred

during the measurements was taken from tables 4-17 and 4-21. It shows that the

average of localised power loss in the limbs was 10% higher than that of the yoke-

045 joint. Whereas under load condition comparing search coil position 8 in the

450-yoke with the search coil position 13 in the limb T-joint, the maximum produced

localised power loss remained higher in the limb by the factor of 32%.

Comparing localised power loss obtained in the T-joint and yoke- 045 joint when the

core energised by PWM voltage excitation at 0.4T under no-load condition, tables 4-

19 and 4-23, comparing search coil position 16 in the yoke- 045 joint with the search

coil position 16 in the limb T-joint, it shows that localised power loss in the limb T-

joint had value of 19% higher than that of the yoke- 045 joint. However, comparing

same search coil positions under load condition, tables 4-20 and 4-24, localised

power loss found to be increased in the limb by 30%, than that of the yoke-450 joint.

Search coil position 16 in the limb T-joint has shown higher value of localised power

loss than search coil position 16 in the 450-yoke joint at all magnetising levels under

load and no-load condition.

Comparing localised power loss obtained in the T-joint and yoke- 045 joint when the

core energised under sinusoidal waveform at peak flux density 0.6T under no-load

condition. Comparing search coil position 3 in the yoke- 045 joint, with the search

coil position 3 in the limb T-joint, tables 4-17 and 4-21 show maximum and

minimum of localised power loss distribution. The variation of the localised power

loss in the limb T-joint was 32% higher than that in the yoke. However, comparing

the result obtained under load condition with the same search coil positions, tables 4-

20 with 4-24. Localised power loss was higher by 37% in the limb joint than that of

the yoke joint.



130

Comparing the result obtained when the core energised by PWM voltage excitation

at 0.6T under no-load condition. Localised power loss in the limb T-joint was 56%

higher than that in the yoke- 045 joint. However, comparing the result obtained under

load condition tables 4-20 and 4.24. Localised power loss in the limb T-joint was

51% higher than that in the 450-yoke joint.

Comparing the result obtained in the limb T-joint with the result obtained in the 045 -

yoke joint, when the core energised at peak flux density of 1.0T under sinusoidal

waveform no-load condition. Search coil position 3 in the limb was compared with

search coil position 3 in the yoke- 045 joint. Tables 4-17 and 4-21, localised power

loss in the limb joint had value of 32%, higher than that in the yoke 450- joint.

However, comparing the result obtained under load condition tables 4-18 and 4-22,

localised power loss in the limb joint has shown higher value than that of the yoke

joint by the factor of 54%.

Comparing the result obtained when the core energised by PWM voltage excitation,

at peak flux density 1.0T under no-load condition tables 4-19 and 4-23. Comparing

search coil position 7 in the limb T-joint with the search coil position 3 in the yoke

045 -joint, localised power loss in the limb joint had a value of 48% higher than that

of the yoke 450- joint. However, comparing localised power loss under load

condition with the same search coil positions, the result have shown that localised

power loss in the limb T-joint has higher value than localised power loss in the yoke

450- joint by the factor of 24%.

In conclusion with the core energised under sinusoidal and PWM voltage excitations

at all magnetising level of peak flux density 0.4T, 0.6T and 1.0T, under load and no-

load conditions, localised power loss in the limb T-joint have shown higher value

than yoke- 045 joint, that is due to the amount of the localised flux flow in the limb

T-joint is higher than the amount of the localised flux flows in the yoke- 045 joint.

Study of the rotational flux was also covered throughout this experiment. Most of the

flux in the middle of the limb areas remained in the rolling direction, rotational flux

was found to be very small in this area. However, T-joint areas had high

concentration of rotational flux, especially near the cutting edge when the flux is



131

expected to be jumping from one side to another side. The major axes of the

localised flux density in the middle of the lamination and the outer joint were mainly

along the rolling direction.

Influence of modulation index and switching frequency on total 4.3.11

power loss in three-phase transformer core.

A secondary winding was connected to a power analyser “Norma D6000 (S/N: ND

58172 RR)”, so the secondary induced voltage was calculated using Fast Fourier

Transform (FFT). Fig. 4-27, 4-28 and 4-29, show assigned value of modulation index

in the range of 0.5, 0.7, 0.8 and 1.2 with assigned value of switching frequency

varied in the range 1 kHz, 2 kHz and 3 kHz respectively. Transformer core was

energised at peak flux density of 1.0T.

Fig. ‎4-23 Total power loss under PWM voltage excitation with assigned value of modulation

index at 3 kHz

0

0.5

1

1.5

2

2.5

3

3.5

0.5 0.6 0.7 0.8 1.2

To

tal

po

wer

lo

ss (

W/k

g)

Modualtion index



132


index at 2 kHz


index at 1 kHz

3.75

3.8

3.85

3.9

3.95

4

4.05

4.1

4.15

0.5 0.6 0.7 0.8 1.2

To

tal

po

wer

lo

ss (

w/k

g)

Modulation index

3.85

3.9

3.95

4

4.05

4.1

4.15

4.2

4.25

0.5 0.6 0.7 0.8 1.2

To

tal

po

wer

lo

ss (

W/k

g)

Modulation index



133

Analysis and discussion 4.3.12

From Fig. 4-23 to Fig. 4-25, the highest loss of the transformer core occurred at the

lowest value of modulation index = 0.5 and 0.6. Nevertheless, it was notice that total

losses were decreased with the increase of modulation index and with increase of

switching frequency . This was caused by higher harmonic contents in the voltage

waveforms produced by PWM inverter at lower values of =0.5 and 0.6.

The highest total losses were seen to be at the lowest values of modulation index

and at the lowest value of switching frequency . An increase of the switching

frequency under PWM voltage excitation caused a reduction in total loss for

example, when 0.5 at switching frequency of 1 kHz were compared to 0.5 at

switching frequency of 3 kHz, the reduction in total power loss were 35 % W/kg.

It can be concluded that low value of and low value of results in increase in

the total losses in transformer core. Beneficial effect was observed with increase of

the modulation index to 1.2 and increase of switching frequency to 3 kHz which led

to reduced total power loss under PWM voltage excitation.



134

CHAPTER 5

5. Introduction

Magnetostriction of core lamination is one of the main sources of transformer

acoustic noise. A measurement system using strain gauge has been designed and

built. This was optimized for magnetostriction measurements under sinusoidal and

PWM voltage excitations.

Historically Five different methods were used to measure magnetostriction properties

of electrical steel which are, Piezoelectric displacement transducer, linear variable

differential transformer, capacitive displacement sensors, laser doppler techniques

and resistance strain gauge. Results show reasonable correlation between those

methods.

In this study the influence of localised magnetostriction of 3% grain-oriented silicon

steel was investigated under sinusoidal and PWM waveforms under on load and no-

load conditions, with the different peak flux densities.

Magnetostriction 5.1.1

In 1842 James Joule had discovered that ferromagnetic material changes it is length

when subjected to external magnetising field. He proved that by magnetising iron bar

the length of the iron bar increases due to the change in the domain wall position as it

starts to move from it is original position to a new position [23]. He also discovered

that magnetostriction can be positive or negative. If the length of the iron bar

increases with increasing the external magnetising field, then magnetostriction

termed as positive . Whereas, if the length of the bar decreases with increasing the

external magnetic field, margentstriction is termed negative . However, after

reversing the direction of external applied magnetizing filed the sign of does not

reserve. This results in magnetostriction having fundamental frequency of twice that

of the excitation frequency.



135

Domain wall and spontaneous magnetostriction 5.1.2

Discorded magnetic moments interaction produce force between atoms that tends

to strain lattice anisotropically, a magnetic material is deformed due to the magnetic

interaction. This deformation is explained by an asymmetric tensor of elastic

distortion, this effect can be observed under microscope [55]. When ferromagnetic

material is heated above its Curie temperature and then cooled, domain wall will

have completely random alignment of magnetisation which ensures that the bulk

magnetisation within the whole volume is zero as shown in Fig. 5-1 (a). Whereas,

when material goes below the Curie temperature it becomes ferromagnetic. As solid

cooled below the Curie temperature, spontaneous magnetisation occurs within the

domains and this produces spontaneous magnetostriction along particular direction as

shown in Fig. 5-1 (b). At this point the amplitude of the magnetostriction is

independent of crystallographic direction within each domain.

Fig. ‎5-1 Mechanism of magnetostriction



136

The spontaneous magnetostriction along the direction of the domain magnetisation is

equal to the saturation magnetostriction ‘ and will cause magnetoelastic energy

‘ this can be calculated using the following equation:

2sin

2

3SE (5.1)

Where is the angle between the direction of magnetisation and direction of the

applied stress .

The average deformation throughout the cubic crystal such as silicon iron can then

be obtained by using following equation which is widely known as Becker-Doring

equation [56] assuming that the domains are oriented in random:

)(3)3

1(

2

3313132322121111

2

3

2

3

2

2

2

2

2

1100 (5.2)

Where 1 , 2 and 3 are the directional of cosines of the magnetisation direction

and 1 , 2 and 3 are the directional cosines of the strain-measurement direction

with respect to the cube edges. 100 and 111 are the saturation magnetisation

constants in the [100] and [111] directions respectively [56].

Saturation magnetostriction 5.1.3

Saturation magnetostriction is the fractional change in length between a

demagnetised ferromagnetic solid and the same solid in a magnetic field. In order to

obtain saturated value in ferromagnetic material magnetic, field needs to be

sufficiently strong to saturate the magnetic material along the direction of the applied

field as shown in Fig. 5-1 (c). The applied magnetic field causes the domains to align

in parallel and hence the strain are parallel as shown in Fig. 5-1 (c) [2].



137

Transformer noise 5.1.4

Recent study to develop transformer core efficiency are not restricted to lower losses

but are also focused on lower noise. The increasing energy demand brings

transformers closer to the population which makes the noise problem more and more

important. Transformer core noise is emitted from winding noise, magnetic core

vibration and core construction and core design [57].

5.2 Winding noise

Winding noise is classified as load noise or current noise because it is caused by the

current passing through the winding and the total current of the other winding.

Winding noise can be reduced by having good guilty winding wrapped precisely

around the core [58].

Fans and pump noise 5.2.1

The other source of the noise in transformers is generated from cooling fans or

pumps, as transformer loss will mostly have converted into heat. As a result,

insulating medium inside the transformer, usually oil is used to remove the heat from

winding and transformer core [59].

Magnetic core vibration 5.2.2

Core vibration is produced by magnetostriction and magnetic force which is known

as the (Maxwell force). Due to the extension and contraction taking place all over the

laminations each lamination behaves unpredictably with respect to its neighbour.

Magnetic core vibration is identified as the biggest sources of noise [60].

Core construction and design 5.2.3

Transformer core is assembled by using many laminations having a distributed mass,

with different movements occurring all over the core. Each lamination has different

association mode. Nevertheless, mitred joints which introduce mechanical problems

are hard to analyse [61].



138

Present study shows that strain of the core is the primary source of the core noise,

nevertheless, strain occurs in the core resulting from magnetostrirtion. The

magnitude of the magnetostrictive properties depends on the type of material and

applied magnetic field.

Magnetostriction characteristic under applied field 5.2.4

Magnetic domains in ferromagnetic material are strained in the direction of

spontaneous magnetisation as result of applying external field, any rearrangement of

the domain structure will change the net strain of the material. Nevertheless, this

would cause the direction of the internal field within the domains to rotate to the

direction of the applied field. Fig. 5-2 [62].

Fig. ‎5-2 Domain walls rotate to the applied field



139

So, it can be noticed that domain wall is the primary reason for magnetostriction in

the ferromagnetic materials.

5.3 Method used to measure magnetostriction

There are several methods used to measure magnetostriction which are: Piezoelectric

displacement transducer, linear variable differential transformers, capacitive

displacement sensors and laser Doppler techniques.

Piezoelectric displacement transducer 5.3.1

Piezoelectric displacement transducer consists of stylus pin mechanically linked to

the piezoelectric bi-morph. Attaching the leads of the pin on the lamination surface.

Fig. 5-3, changes of the charge being developed in the element. This method is used

to measure well defined point and it is impossible to measure all areas

simultaneously [63].

Fig. ‎5-3 Magnetostriction measurement systems using piezoelectric transduces technique



140

Linear variable differential transformer 5.3.2

Linear variable differential transformers (LVDT) can be used to measure

magnetostriction, it consists of movable core with one primary coil and two

secondary coils. The core is placed inside the coils at the centre. Fig. 5-4 and then

sinusoidal excitation current applied to the primary winding which is coupled to the

secondary winding by the movable core. The two secondary coils are identical.

Movement of the core would cause a flux leakage in the secondary coils. When the

core is moved away from the centre position, a differential voltage appears across the

secondary coils then the displacement can be measured with the use of phase

sensitive detector. Detecting of magnetostriction occurs when the core moves from

its position, then sensitive detector gives an output proportional to the change which

has occurred [64].

Fig. ‎5-4 Schematic diagram of LVDT



141

Capacitive displacement sensors 5.3.3

Capacitive displacement sensors generate an electrical signal as a result of the elastic

deformation of a membrane and consist of an oscillator circuit and two plates

separated by distance usually air. One of the plates is attached to the free end of the

lamination whilst the other one is fixed. Vibration in the lamination produces a

voltage signal proportional to the change in length of the specimen [65].

Laser Doppler techniques 5.3.4

Laser Doppler techniques was first presented by Nakata [66]. The magnetostriction

displacement is measured by two mirrors mounted on the sample. Fig. 5-5. The laser

beam is divided into two beams by the half mirror . The beam a1 has its

frequency shifted by an amount Beam a2 is reflected from mirror fixed on the

sample, the output current is produced from a photoelectric detector. FM decoder

gives a signal proportional to the velocity of sample vibration.

Fig. ‎5-5 Block diagram of a laser doppler velocimeter



142

In this project strain gauges were used to study localised magnetostriction in the

transformer core. Strain gauges were employed in the middle of the transformer core

where the stress in highly present. And hence magnetostriction was measured due to

the change occurred in the electrical resistance of strain gauge. There are two types

of strain gauge used to measure localised magnetostriction, pro foil strain gauge and

three-wire strain gauge.

5.4 Pro foils strain gauges

Type of strain gauge used to measure localised magnetostriction has a gauge length

of 8 mm wound with gauge width of 4 mm, its gauge factor was approximately 2.1

and gauge resistance of 120 . The strain gauge is usually cemented to the polyimide

backing which has a withstand temperature of up to C0180 , making them ideal for

higher temperature applications and gives excellent bonding as shown in Fig. 5-6.

Fig. ‎5-6 Pro Foil strain gauge used to Measure magenetostriction



143

Three-wire strain gauge rosettes pre-wired 5.4.1

In order to study the strain in the core and bending effect of the lamination, pre-wired

strain gauge was glued on both sides of the lamination. It was used to cover more

area in the plane of the lamination as it was bigger than Pro Foil Strain Gauge as

shown in Fig. 5-7.

Pre-wired strain gauge has three measuring electrical wire positioned in different

axes which is composed on polyimide film. With gauge length of 10 mm, gauge

width of 20 mm, gauge factor of 2.10 and gauge resistance of 120 .

Fig. ‎5-7 Shows 3-Wire Strain Gauge Rosettes Pre-wired

Transformer core was energised by three-phase sinusoidal supply and PWM inverter

with different peak flux densities under load and no-load conditions. Measurements

were taken simultaneously with respect to the energising condition, data logger “700-

128-SM” was used to measure and store localised magnetostriction.



144

Strain data logger 5.4.2

Localised magentostriction was measured by, strain data logger “700-128-SM” when

the core was energised by PWM inverter and sinusoidal voltage excitation. Figure

5.8 shows the measurement system, after carefully building the transformer core,

strain gauge soldering attachment wires were connected to the data logger via

terminal connector as shown in Fig. 5-8. Insulation of the attachment wires at the

ends were removed very carefully. Moreover, attachment wires were twisted

separately to avoid picking up any stray noise voltage.

Strain data logger has 80 channels which is can be used to measure large numbers of

strain gauges simultaneously and also helps to connect specimen attachment wires

straight to the channels.

After connecting attachment wires to the channel, it would be necessary to highlight

selected channel this is can be done through the personal computer. However, strain

data logger has unique advantages which allow you to know which is fault and active

strain gauges by pressing the calibrate bottom. After calibrating strain gauges, it

would be necessary to obtain initial balance of the specimen for each experiment and

this obtained by potentiometer inserted between active and dummy gauges this is

also known as the “apex resistance”.

After selecting desired channel and checking all strain gauges are calibrated. A

galvanometer is tapped into the resistance, at the balance point reading of

measurement can be taken by pressing alarm bottom which would record any change

occur in the resistance. However, monitoring and collecting data can be done through

personal computer which would indicate any changes occur in the electrical

resistance, for each measuring circuit it is necessary to calibrate and rebalancing

strain gauges repeatable.



145

Fig. ‎5-8 Strain gauges measurement system



146

Strain gauge sample preparation 5.4.3

Firstly, locations of strain gauges were marked on the laminations on both rolling RD

and TD directions (limbs, yokes, corners and T-joint) then, insulating coating on

these areas was removed very carefully to avoid any stress or roughness on the

surface which was then cleaned by using acetone. A drop of strain gauge special

adhesive was applied on the surface, and then a gauge was stuck by pressing its

whole area uniformly for a few minutes, until the adhesive was dry.

Nevertheless, wires used in this experiment were 0.08mm2 paralleled vinyl lead wire

with a very low resistance of 0.44 Ω. The ends of the wires were soldered to the

strain gauges through soldering terminal and then they were terminated to the logger

through the input of the terminal connector. The output of the terminal connector was

connected to RJ45 plugs and then the output voltage was passed to the logger

through the logger measuring channel. Fig. 5-9 shows strain gauge measurement

procedures connection. The soldered points were flattened as much as possible. The

gauges and their leads were completely insulated from the lamination surface.



147

Fig. ‎5-9 Strain gauges measurement connection

As two type of strain gauges were employed in this work, transformer core was

carefully mantled and dismantled twice. Nevertheless, position of strain gauges were

varied Pro Foil Strain Gauges were cultivated on one side of the lamination on the

other hand three Element Strain Gauges were cultivated on both sides of the

lamination so that the bending effect due to the building factor and clamping pressure

could be measured. Fig. 5-10 and 5-11 show position of Pro Foil Strain Gauges and

Three-Wires Strain Gauges respectively.



148

Fig. ‎5-10 Positions of pro foil strain gauges selected position



149

Fig. ‎5-11 Positions of three-wire strain gauges Roesttes pre-wired



150

Strain gauges were glued on both sides of the lamination and in both directions,

rolling and transvers directions (RD and TD), to measure localised magnetostriction

and to measure the bending effect in the transformer core as shown in Fig. 5-11. The

small length of the conductor in the direction at right angles to the axis of the gauge

impart some degree of sensitivity to transvers strain, but this effect is small enough to

be neglected. However, the resolution of the strain gauges is always in the range of

X , which is reasonably sensitive for magnetostriction measurement. Strain

gauge has advantages and disadvantages over the other techniques.

Advantages

1. Low cost

2. Localised measurement

3. High resolution measurement

Disadvantages

1. Time consuming

2. Preparation arrangement

3. Hard to place the gauge in required direction

In order to avoid any change of the strain electrical resistance (due to normal

pressure), pieces of tough rubber (15 mm × 5 mm ×1 mm) were glued around each

strain gauge and all over the test lamination. These pieces of rubber did not introduce

any additional stress because of their flexibility. Fig. 5-12 and 5-13 show schematic

diagram of the arrangement [67].



151

Fig. ‎5-12 Position of the robber placed around Pro-foil strain gauges

Fig. ‎5-13 Position of the robber placed around three- wire strain gauges Rosettes pre-wired



152

Magnetostriction calculation 5.4.4

Pro foil strain gauges and three-wire strain gauges rosettes pre-wired are placed on

material in which they allow their electrical resistance to measure localised

magnetostriction. As the test specimen extends or contracts under stress, a

corresponding increase or decrease in electrical resistance. The alteration in

resistance is, within wide limits, proportional to the strain in the specimen, that is:

=

.

[67] (5.3)

Where is the strain

K is the gauge factor and Ro is the gauge resistance (120 Strain can be

calculated by altering the resistance of the gauge. So hence the change in resistance

produces a change in the output voltage.

On the basis of change of length and cross-sectional area only, it can be shown that

the gauge factor is (1 + 2 , where is Poison’s ratio [68]. For most materials the

specific resistance of the conductor changes with strain and the gauge factor is

usually about 2.0. Tables 5-1 to 5-8 show the direction of the strain gauges and

calculated values of the strain within the transformer core.



153

5.5 Investigation of localised magnetostriction within transformer core

Investigation of magnetostriction within the core has been carried out when the core

was placed horizontally. Transformer core was energised with different peak flux

densities under sinusoidal and PWM voltage excitations. Strain gauges were

positioned in the middle of the core, assembled on several test laminations. As top

half of the core has been removed then layers of the prepared laminations have been

placed in the middle of the core over the lower half and then the top half has been put

back very carefully. The corner joint was precisely adjusted with a Vernier, the core

was then clamped together at a pressure of 0.5 Nm. Table 5-1 to table 5-4 shows

magnetostriction measurement using Pro foil strain gauge when transformer core was

energised by sinusoidal and PWM waveforms respectively.

To obtain wide knowledge about the operation of transformer core it is necessary to

determine the strain that occurs in the laminations, as the transformer laminations are

very stress sensitive. Furthermore, as the transformer core was mantled and

dismantled for couple of times, the bending affect was unavoidable.

To study the bending effect of transformer core Three-Wire Strain Gauge Rosettes

Pre-wired were cultivated on both side of the lamination as shown in fig. 5-11. Data

logger was again used to monitor the changing value occurred in the electrical

resistance of the strain gauges. Table 5-5 to table 5-8 show the value of bending

effect occurring in the transformer core.



154

Table 5-1 Localised Pro foil strain gauges strain measurements with the core placed in

horizontal position under sinusoidal waveform with various peak flux densities, at 0.5Nm

clamping pressure


horizontal position under PWM waveform with various peak flux densities, at 0.5Nm clamping

pressure

Core

flux

Densities

(T)

Strain gauges positions Strain (ppm)

R1 2T 3R 4R 5R 6T 7R 8R 9R 10R 11T 12T

0 0.02 0.02 0.06 0.04 0.4 0.04 1.3 1.5 0.02 0.6 0.02 0.02

0.4 0.4 0.3 1.1 0.9 1.5 0.8 2.1 2.9 0.7 1.9 0.4 0.6

0.6 0.9 0.5 1.9 1.4 2.2 1.3 2.8 3.4 1.2 2.5 1.0 1.1

1.0 1.5 1.2 2.4 2.2 2.9 2.1 3.9 4.5 2.0 3.2 1.6 1.8

Core

flux

Densities

(T)


R1 2T 3R 4R 5R 6T 7R 8R 9R 10R 11T 12T

0.4 1.3 3.6 3.6 3.4 3.9 2.9 4.3 6.4 2.4 4.1 2.1 2.3

0.6 2.7 1.9 5.3 5.1 5.7 4.5 6.4 6.6 4.3 6.1 3.3 3.8

1.0 2.7 2.2 5.5 5.5 6.2 5.1 7.3 7.7 5.3 7.8 5.9 4.7



155

Table 5-3 Localised Pro foil strain gauges strain measurements with the core placed in vertical

position under sinusoidal waveform with various peak flux densities, at 0.5Nm clamping

pressure


position under PWM waveform with various peak flux densities, at 0.5Nm clamping pressure

Core

flux

Densities

(T)


R1 2T 3R 4R 5R 6T 7R 8R 9R 10R 11T 12T

0.4 2.7 2.6 0.5 0.5 1.7 1.5 5.2 3.3 1.6 4.8 3.5 4.3

0.6 3.6 3.7 1.3 1.4 2.8 1.8 6.3 1.8 1.5 7.6 4.6 5.6

1.0 4.7 4.5 1.7 1.7 3.2 3.2 7.8 4.6 3.6 9.7 5.2 7.5

Core

flux

Densities

(T)


R1 2T 3R 4R 5R 6T 7R 8R 9R 10R 11T 12T

0.4 4.7 4.8 1.4 1.6 4.8 3.8 6.9 4.8 3.4 6.8 5.3 6.6

0.6 5.5 6.6 2.5 2.8 6.2 5.5 8.9 6.8 6.3 9.3 7.3 8.5

1.0 9.3 7.8 3.4 3.6 7.8 5.8 12.6 7.8 7.3 13.9 9.6 12.3



156

Table 5-5 Three-wire strain gauges strain Rosettes Pre-wired measurements with the core

placed in horizontal position under sinusoidal waveform with various peak flux densities, at

0.5Nm clamping pressure

Core

flux

Densities

(T)

Strain gauge positions strain (ppm)

1 2 3 4 5 6 7 8 9 10

0 0.02 0.02 0.4 0.6 3 4 1 2 2 0.08

0.4 0.4 0.7 1.8 2.6 6.7 7.3 4.3 4.3 5.8 0.7

0.6 0.9 1.3 4.0 5.4 8.5 9.4 6.7 6.7 7.8 1.7

1.0 1.6 2.4 5.1 7.5 14.6 15.1 11.7 11.1 13.8 2.8


horizontal position under PWM waveform with various peak flux densities, at 0.5Nm clamping

pressure

Core

flux

Densities

(T)


1 2 3 4 5 6 7 8 9 10

0.4 1.5 2.3 5.3 5.8 8.4 9.3 7.2 7.5 8.1 3.1

0.6 1.9 2.8 8.2 9.5 10.7 12.1 11.7 11.2 14.3 4.9

1.0 2.6 3.4 10.8 12.7 15.6 15.3 15.8 15.3 16.1 4.9



157

Table 5-7 Three-wire strain gauges strain Rosettes Pre-wired measurements with the core

placed in vertical position under sinusoidal waveform with various peak flux densities, at 0.5Nm

clamping pressure

Core

flux

Densities

(T)


1 2 3 4 5 6 7 8 9 10

0.4 4.3 5.5 1.3 4.8 7.6 6.8 6.9 8.3 8.8 6.6

0.6 6.3 6.5 3.2 6.8 9.7 8.3 12.7 12.3 12.6 13.6

1.0 10.4 9.6 4.8 9.7 15.5 14.9 16.3 15.2 16.9 15.2


position under PWM waveform with various peak flux densities, at 0.5Nm clamping pressure

Core

flux

Densities

(T)


1 2 3 4 5 6 7 8 9 10

0.4 5.5 5.9 4.2 6.7 6.9 6.7 9.5 9.4 9.5 13.7

0.6 7.7 8.3 6.8 9.8 11.8 12.3 13.1 13.7 13.8 16.2

1.0 9.4 9.6 8.3 13.8 17.8 16.8 17.3 17.5 17.9 18.6



158

Stress 5.5.1

Stress is the internal forces reacting to external force exerted at a body’s surface

[5.1]. As it has been known, magnetic properties of ferromagnetic materials such as

permeability, magnetostriction and power loss are sensitive to mechanical stress. The

ferromagnetic domain pattern of a crystal, which is an indicator of its magnetic

properties, changes with changes of strain of the crystal due to the applied stress. As

long as the applied stress is within the elastic range of the material, the original

pattern returns after unloading the applied stress.

Depicts a slice of material with infinitesimal thickness in equilibrium when external

force is applied, the internal force will react to the applied external force and that

would cause stresses normal and tangential to the material.

Stress calculation 5.5.2

The measured strains were converted to stresses by using theoretical Young's

modulus [69] values. The commonly used Young's modulus for perfectly grain

oriented steel are:

= 1.17 × 105

MN/m2 (5.2)

= 2.14 × 105

MN/m2 (5.3)

Where and are the Young's modulus in rolling and transverse directions

respectively. Tables 5.1 to 5.8 show the direction of the strain gauge and calculated

values of the strain within the transformer core.



159

Noise and vibration phenomena in transformer core 5.5.3

The causes of transformer core vibration are magnetic force between laminations and

lamination deformation due to magnetostriction. If a transformer core has

homogenous structure, there is only in-plane vibration due to magnetostriction.

However, as the transformer core is usually built from stack of lamination, there is a

vibration in an out-plane direction due to the magnetic force[70]. If transformer core

lamination is magnetised and magnetic flux flows uniformly along the rolling

direction, the deformation due to transverse magnetostriction is neglected by

approximately 5 times and magnetostriction in the rolling direction is higher than in

the transverse direction when flux flows uniformly along the rolling direction [71].

Considering the dimensions of the three-phase transformer core, there are three

different shapes for three-phase flux densities as shown in Fig. 5-14 [72]. Each limb

of a three-phase core is magnetised with 1200 phase shift [73]. Top and bottom yokes

which are interlaced to the limbs have associated magnetic flux with the limbs.

Fig. ‎5-14 Three-phase magnetic flux density waveforms [20]



160

As each phase is magnetised with 0120 angle phase difference so hence different

movement take place in the core and hence magnetostriction is resulted all over the

core as magnetostriction is proportional to induced voltage.

Influence of magnetic flux density on transformer core magnetostriction 5.5.4

and vibration

Magnetic flux density was set with different peak flux densities in order to study its

effect on magnetostriction and core vibration. Localised magnetostriction increased

when the magnetic flux is increased from 0.4T, to 0.6T and 1.0T. The significant

increase of localised magnetostriction is due to the effect of change in the domains

structure due to the applied voltage. This affects the magnetic force and vibration to

increase, and increases localised magnetostriction as shown in tables 5.1 to 5.8.

It could be concluded that when operating the core at low magnetic flux density, the

noise and vibration are less than operating at high flux density. This can reduce the

core noise and vibration. However, this leads to an increase in cost and larger core

size.

5.6 Core vibration and sound level measurement (SPL)

Sound is defined as any pressure variation that human ear can detect, which is

created when objects vibrate, the range of magnitude from the faintest to the loudest

sound the ear can hear is so large that sound pressure is expressed on a logarithmic

scale in units called decibels ( ). The decibel as used in acoustic is a measurement

comparing the pressure generated by a noise against some standard level [74].

In order to make measurements of a acoustic noise generated at particular point in

transformer core stress was converted to sound pressure level by using equation 5.4.

Therefore, the sound pressure level (SPL) is given as

)(log20 10

ref

meas

P

PSPL ][dBA [74] (5.4)



161

Where measP is the measured A-weighted sound pressure level, and refP is the

reference sound pressure level and equal to 20 . Standard measurements use the

A-weighted sound pressure level as a measured variable and measurements on

transformers are made under no-load condition.

Analysis and Discussion 5.6.1

Magnetostriction distribution in the grain-oriented material is almost independent of

the type of material, applied magnetic field and type of magnetization. Attempt has

been made to analyse localised magnetostriction within the core under sinusoidal and

PWM voltage excitations. Experiments were accomplished on a three-limb model

transformer core with different peak flux densities of 0.4T, 0.6T and 1.0T. The core

was stacked of HGO material which was built with laminations of 100 mm wide, 0.3

mm thick. These experiments have been carried out with the core placed in a

horizontal position and then measurements were repeated with the core placed in the

vertical position.

Localised magnetostriction under PWM and sinusoidal voltage excitation 5.6.2

in three-phase transformer core in horizontal position

As the core was assembled and dismantled few times the bending of the yoke and

limb was unavoidable. Tables 5.1 to 5.8 shows localised strain in central layer of the

core. These measurements were taken under sinusoidal and PWM conditions when

the core was placed horizontally and vertical. Torque wrench was used to set the

clamping pressure of 0.50MN/ .

Under Pro Foil Strain Gauges table 5.1 shows the localised distribution of peak to

peak values for the total of 12 strain gauges, placed in different regions nine in the

RD and three in TD. At 0.4T under sinusoidal and PWM voltage excitation the

highest compressive strain of 2.9 and 6.4 ppm was obtained at strain gauge number

(8) in the RD near the T-joint in the yoke. However, when the flux density was

increased to 0.6T, compressive strain of 3.4 ppm under sinusoidal voltage excitation

was observed in strain gauge number 8, with the core energised under PWM

compressive strain of 6.6 ppm was observed in strain gauge number 8. Increasing the

flux density to 1.0T, same trend of result was obtained, strain gauge number 8



162

represents large magnitude of localised strain. It was increased to be 4.5ppm under

sinusoidal and 7.7ppm under PWM voltage excitation.

Further away from yoke T-joint strain gauge position 7 was compared with strain

gauge position 8 at peak flux densities of 0.4T, 0.6T and 1.0T under sinusoidal

voltage excitation, their strains reduced by approximately 27%, 17% and 13%

respectively.

Comparing the result obtained at corner joint strain gauge position 4 with strain

gauge position 5 under sinusoidal and PWM voltage excitations, under sinusoidal

excitation at 0.4T, 0.6T and 1.0T strain gauge position 5 has higher values of

localised strain by the factor of 40%, 36% and 24% respectively. However, result

obtained under PWM voltage excitation shows higher value of localised strain

occurred in strain gauge position 5, at 0.4T localised strain was higher by 12%. At

0.6T localised strain was higher by 10% and at 1.0T localised strain was higher in

strain gauge position 5 by 11%.

Comparing the result obtained in the outer limb with the result obtained in the central

limb, strain gauge position 1 with strain gauge position 12 in the rolling direction.

Under sinusoidal and PWM voltage excitation strain gauge position 12 shows higher

value of localised strain at all magnetisation levels. For example, with the core

energised under sinusoidal voltage excitation at 0.4T, localised strain was higher by

33% in strain gauge position 12. Increasing the flux density to 0.6T and 1.0T strain

gauge position 12 shows higher localised strain than strain gauge position 1 by the

factor of 18% and 16% respectively. Comparing strain gauge position 1 with strain

gauge position 12 under PWM voltage excitation at 0.4T, 0.6T and 1.0T strain gauge

position 12 shows higher localised strain by factors of 43%, 28% and 42% higher

than the localised strain occurred in strain gauge number 1.

In order to study the bending affect induced in the transformer core three-wire

Rosettes Pre-wired strain gauges were employed on both sides of the lamination,

tables 5.5 and 5.6 show the value of bending effect and the value of localised

magnetostriction. However, higher bending value recorded near the T-joint in the

yoke strain gauges number 5 and 6 whereas, smallest value of localised strain was

obtained in the middle of the outer limb strain gauges number 1 and 2.



163

Away from the middle limb and middle yoke, comparing localised strain

measurements in the limb and yoke corner joints strain gauges position 4 and 5.

When the core energised under sinusoidal voltage excitation at 0.4T, 0.6T and 1.0T,

tables 5.1 and 5.2, it can be seen that yoke corner joint has shown large values of

localised strain than the outer limb. For example, at 0.4T, yoke corner joint had a

value of 40% higher than limb joint. Increasing the flux density to 0.6T and 1.0T

again yoke corner joint shows larger value of localised strain by the factor of 36%

and 24% respectively higher than the outer limb. Nevertheless, comparing the result

obtained with the same strain gauges position when the core energised under PWM

voltage excitation at peak flux densities of 0.4T, 0.6T and 1.0T same results were

obtained starin gauge position 5 show higher localised strain than strain gauge

position 4 for example at 0.4T strain gauge position 5 has higher value of 12% than

strain gauge position 4. Increasing the flux densities to 0.6T 1.0T strain gauge

position 5 had a value of 10% and 11% higher than strain gauge position 4.

Discussion on the result obtained under Three-Wire Rosettes Pre-wired strain gauge

with that obtained under Pro Foil strain gauges is as follows. It can be concluded that

the increase of localised strain in the T-joint may be due to the presence of clamps

and also due to the joint-overlapping and imperfect positions of the lamination. The

magnitude of the localised strain in the centre limb was higher than those in the outer

central limb. This was due to the fact that the ends of the outer limbs were held more

firmly than those of the central limb. Further away from the centre, strain gauge

positions 3 and 4 in the limb corner joint at the inner side of lamination, localised

strain was increased. This is mainly because of the clamps and the fact that the effect

of clamping was much higher at the inner edge. Highest localised strain in the

transverse direction was obtained in the strain gauge position 6, for example at 0.4T,

0.6T and 1.0T under sinusoidal voltage excitation it was higher than strain gauges at

position 2 by 62%, 61% and 42%, table 5.1, this is mainly due the larger bending in

that region.

Near the corner and T-joint, higher values of localised strain were obtained. This is

because flux deviation occurred in all directions in the core joint whereas in the limb

flux follows the easy axis, again same results were obtained under load and no-load

conditions.



164

Basically, strain occurred all over the area under PWM and sinusoidal waveforms.

The average value of magnetostriction was higher in the yoke than that in the limb

due to the alternating magnetization. The average of localised strain was higher at

the T-joint than that in the corner joint, this is due to rotational magnetization and the

main direction of strain which is given in RD. However, under the two types of strain

gauges used, localised magnetostriction was higher when the core was energised by

PWM waveform. This is due to the high harmonic contents and due to the shape of

the waveform.

Localised magnetostriction under PWM and sinusoidal voltage excitation 5.6.3

in three-phase transformer core in vertical position

Tables 5.3, 5.4, 5.7 and 5.8 show localised strain in the limbs, yokes and the joint

areas when the core was held in a vertical position. Under sinusoidal voltage

excitation, table 5.3, in the middle regions of the central limb strain gauge position

12, the average of localised strain at 0.4T, 0.6T and 1.0T was 4.3 ppm, 5.6 ppm and

7.5 ppm respectively. While under PWM voltage excitation at magnetising flux of

0.4T was 6.6 ppm, and at magnetising flux density of 0.6T was 8.5 ppm.

Nevertheless, at magnetising flux density of 1.0T it was 12.3 ppm. Away from the

middle region, strain gauge position 10 near the T-joint localised strain was

decreased, for example at 0.4T under sinusoidal voltage excitation it was decreased

by 11%. And under PWM voltage excitation at 0.4T was decreased by 3%. Results

have shown same trend under all magnetising levels, strain gauge position 10 shows

higher value than strain gauge position 12 under both sinusoidal and PWM voltage

excitations. Localised strain was higher near the T-joints than that in the central limb,

this was due to the weights of upper yokes and the weight of the limbs themselves.

In the outer limb localised strain was smaller than that in the central limb. This could

be due to the fact that most of the weight of the yokes was carried by the central

limb. However, comparing the results obtained in the T-joint with the results

obtained in the corner joint under sinusoidal and PWM voltage excitations, the level

of localised strain in the T-joint being much larger than that of the corner joint area.

The average value of the localised strain occurred at the corner limb and yoke joint

was found to be higher in the yoke corner joint under both type of strain gauges and



165

under both type of excitation conditions. For example, at 0.4T under sinusoidal

waveform table 5.3, strain gauge position 5 shows higher value of localised strain

than strain gauge position 4, it was larger by 70%. More increasing of the energising

flux density under PWM voltage excitation and table 5.7, under three-wire strain

gauge at 1.0T, strain gauge position 4 had large value of localised strain by 50%

larger than strain gauge position 3. However, the localised strain of the yoke was

observed to be higher when the core placed in vertical position than horizontal

position. For example, at 1.0T under sinusoidal voltage excitation strain gauge

position 9 had a value of localised strain by a factor of 44% larger when the core

placed in vertical position tables 5.1 and 5.3. When the core energised under PWM

voltage excitation at 1.0T, tables 5.6 and 5.8, strain gauge position 4 shows large

value of localised strain when the core placed in vertical position than that when the

core placed in horizontal position by 7%. Larger under vertical position hence

localised strain was found to be higher than what was observed when the core was

placed horizontally. This increase on localised strain was mainly due to the

introduction of the weight of the upper part of the core.

At the corner joint area, localised strain was found to be higher with the core placed

in horizontal position. Comparing result obtained when the core placed on horizontal

with the result obtained when the core placed in vertical position, strain gauge 4 table

5.1, was compared with strain gauge 4 table 5.3. At 1.0T, under sinusoidal waveform

horizontal position was higher than vertical position by 22%. Furthermore, when the

core energised under PWM voltage excitation, strain gauge number 4 table 5.2 was

compared with the same strain gauge in table 5.4 at 0.6T strain results show that

horizontal position had a value of 45% larger then vertical position.

In general, when the core was placed vertically overall localised strain occurred all

over the transformer core, localised strain was found to be higher in the central limb

and outer limb and also localised strain was found to be higher in the T-joint area and

in the yoke area. On the other hand, localised strain was found to be higher in the

corner joint when the core was placed in the horizontal position so it could be

concluded that the overall localised strain was higher in the yoke area when the core

was placed in vertical position, because of the weight of the core.



166

CHAPTER 6

6. Measurement with the Epstein Frame

Epstein frame which is sometimes called Epstein square has been invented by

Epstein in 1900, and it was made as 50 cm square. Later in 1936 Burgwin has

invented smaller size of Epstein frame with 25 cm square. Nevertheless, Epstein

technique works in such a way by placing the Epstein strips between the limb and the

yoke. In this step, clamping pressures were obtained through the limbs and yokes.

However, corner joint in four-lamination Epstein frame is always double-lapped joint

because it provides good and reproducible flux enclosure. Schematically diagram of

Epstein frame is shown in Fig. 6-1.

Fig. ‎6-1 Epstein frame and double overlapped joints



167

There are four fixed windings connected in series. The primary winding is connected

to the power source to provide magnetising current and the secondary winding is

connected to a voltmeter to measure the induced voltage and hence peak flux density.

In the closed sample, the magnetic path length is 0.94 m, as specified in standard

IEC 60404-2, and the instantaneous magnetic field strength ( was measured inside

the labVIEW programme using equation (6.1).

(6.1)

Where )(tI is the primary current, N is the number of turns on the primary winding

and is the magnetic path length. The instantaneous flux density was obtained

from equation (6.2)

(6.2)

Where is the cross- sectional area, is the number of the secondary winding,

is the voltage measured across the secondary winding. By using this method

there will be choice for selecting the most suitable material under different

frequencies and different peak flux densities.



168

Single Strip Tester measurement 6.1.1

The experiment was carried out on single strip tester (SST) using HGO electrical

steel material. Three strips were cut from the limb and two strips were cut from the

yoke from the same batches used to construct the transformer core at (30 mm x 250

mm), and then annealed to relieve stress which occurred during the cutting process.

Measurement of total power (W/kg) were taken under PWM and sinusoidal

excitations. At core flux densities of 0.4T, 0.6T and 1T, both measurements were

carried out under different peak of magnetising frequencies of 10, 25, 50, 100, 200

and 400 Hz. Using measurement controlled system as shown in Figs. 6-2. and 6.3

which consists of a computer, LabVIEW version 8.5 software, “NI PCI 6120” DAQ

card, a power amplifier and a 1 Ω shunt resistance [75].

Each component of the measurement system has a specific different function, for

example the magnetising voltage was generated by the LabVIEW programme via

output voltage of the DAQ card. However, data was taken through LabVIEW

programme which uses mathematical analysis in real time to process the

measurement data and displays the desired output in real time.

In the magnetising core of the SST double vertical cores are used each core was

made from GO steel laminations. A 250 turns of the secondary winding was

wound around a plastic former and 865 turns of primary winding ( ) was wound

around the secondary winding. Then sample was placed between the yokes as shown

in Fig. 6-4.



169

Fig. ‎6-2 Schematic diagram of computer-controlled Single Strip Tester (SST)



170

Fig. ‎6-3 Measurement system of single strip tester



171

Fig. ‎6-4 Single strip tester



172

Power loss in electrical steel based on two-term formula 6.1.2

Power loss in electrical machine plays large role to determine the grades and the

price of material. The power loss in magnetic material depends on four different

parameters which are: frequency peak flux density (( ), thickness of the

material ( and material resistivity (

Power loss due to time-varying magnetic field was separated into two main terms:

hysteresis losses (also referred to as static losses) and eddy current losses

which is also split into classical and anomalous losses (also called excess loss) [76]

then the total loss is given by:

= + =

(W/kg-1

) (6.3)

Where is the hysteresis losses and is normally defined by the enclosed hysteresis

loop as shown in Fig. 1-2 is the eddy current loss which also known as (dynamic

losses). is the coefficient for hysteresis loss and is the coefficient for eddy

current loss. is the magnetising frequency , is the peak flux density and

is Steinmetz constant equal to 1.6.

This method is used when alternating magnetic field is applied to magnetic material,

the area enclosed by hysteresis loop represents a total core loss per cycle.

It is believed that hysteresis loss is due to energy dissipated when domain wall is

moving through the material during magnetisation process. This loss is largely

influenced by stress, impurities, dislocations, and surface roughness. Hence, these

factors have a large impact on the magnitude of the material permeability.

It should be noted that hysteresis losses per cycle is frequency independent, hence

this equation is only valid for low frequency, because at higher frequency magnetic

field distribution is not uniform, maximum at the surface and minimum at the centre

which is known as the skin effect [45].



173

Power loss in electrical steel based on three-term formula 6.1.3

Bertotti [45] explained excess losses based on statistical loss theory. The difference

between two-term formula and there-term formula is that third term is added which

represents excess loss, so the total core loss is expressed as

=

(6.4)

The three coefficients ( , , ) given in equation (6-4) can be obtained from

the measured core losses at different frequencies and flux density range. The excess

losses are mainly related to the non-uniform distribution of the magnetic field inside

the lamination, it depends on the material microstructure, conductivity and the cross-

sectional area.

6.2 Loss separation using extrapolation method based on the two-term

formulation

The extrapolation method is usually implemented to separate the core loss

measurement at different frequencies, in this method the hysteresis loss is separated

by extrapolating core loss per cycle versus magnetising frequency curves at different

flux densities to zero frequency. Therefore, the power loss at zero frequency

represents the static hysteresis loss per cycle. Dividing equation (6.3) by the

magnetising frequency leads to [77].

=

+

=

(6.5)

This equation is a linear function of magnetising frequency at peak flux density

and can be written as:

= (6.6)

Where is the hysteresis loss per cycle and

eddy current

loss. More detailed information for calculating these coefficients are available [78]

[79] [80].



174

Loss separation using extrapolation method based on the three-term 6.2.1

formulation

The extrapolation method is also applicable to separate loss components in the three-

term formulation dividing (6.4) by the magnetising frequency leads to.

=

+ +

√ (6.7)

The latter term is largely influenced by intricate phenomena related to

microstructural interaction, magnetic anisotropy and non-homogenous. Locally

induced eddy current [78] so that at constant coefficients of equation (6.7) can be

written as:

√ (6.8)

Where = , =

and = ). More achievable method

can be used to obtain the coefficients by plotting core loss per cycle versus the

square root of the magnetising frequency √ , for different value of peak flux

density therefore equation (6.8) can be modified by [79]:

√ √ (6.9)

Where and are the coefficient of power loss components and can be obtained

by nominal curve fitting. Using equations (6.7) and (6.8) we have:

Therefore, applying this method for a given flux density, the loss coefficients

and can be obtained. In summary from equation (6.3) to (6.8), it can be

concluded that in the extrapolation method, hysteresis loss per cycle is assumed to be



175

frequency independent and eddy current power loss per cycle is assumed to be a

linear function of frequency. Therefore, the total hysteresis loss can be calculated by

multiplying the hysteresis power loss per cycle by the operating frequency and the

total eddy current power loss is calculated by multiplying the eddy current power

loss per cycle by square root of the operating frequency √ .

Experimental results under PWM voltage excitation at 0.4 T 6.2.2

Power loss measurements were taken under sinusoidal and PWM voltage excitations

on five strips (HGO) material using Epstein size laminations and were tested using

the measurement system as described in part 5.3.4. The power loss results under

PWM flux waveform were compared with those at the same peak flux densities

under sinusoidal voltage excitation. Measurements of power loss of HGO were

carried out at peak flux densities 0.4T and 1.0T respectively, table 6.1 shows total

power loss per cycle with magnetising frequencies of 25, 50, 100, 200 and 400 Hz.

Table ‎6-1 Power loss per cycle under PWM voltage excitation at 0.4 T at different magnetising

frequencies

Magnetising frequency

Hz

Measured power loss

(W/kg)

Power loss per cycle

(W/kg). sec

25 0.098 0.0039

50 0.421 0.0084

100 1.229 0.0123

200 3.212 0.0160

400 6.753 0.0168

Specific power loss per cycle is plotted against the square root of frequency as shown

in Fig. 6-5. On this graph, power loss components obtained by applying a polynomial

curve fitting in Microsoft Excel are plotted.



176

Fig. ‎6-5 Specific power loss per cycle versus square root of frequency at 0.4T under PWM

voltage excitation

By applying the coefficients in equation (6.8), the power loss coefficients are

automatically calculated as shown in table 6.1

Eddy current loss and hysteresis loss versus magnetising frequency are shown in Fig.

6-6. Hysteresis loss is deduced from the static hysteresis loops, and the value of eddy

current power loss per cycle is a linear function of magnetising frequency and can be

obtained using equation (6.10). However, the value of hysteresis and eddy current

loss per cycle is shown in Fig. 6-6.

32222

//..6

mkgWBfdD

p pke

(6.10)

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



177

Where is the peak flux density (T): is the frequency (Hz) is the resistivity (

Ω.m). D is the density (kg/m3) and is the thickness of the lamination [80]. The

thickness and the resistivity have significant impact on the eddy current power loss

hence; small thickness and high resistivity will reduce the power loss.

Table ‎6-2 Measured and total power loss component of Epstein size lamination under PWM

voltage excitation at 0.4T with different magnetising frequencies

Frequency

(Hz)

Measured

power loss per

weight(W/kg)

Pe

(W/kg)

Ph

(W/kg)

Pa

(W/kg)

Pt =

Pe+Ph+Pa

(W/kg)

25 0.098 0.0562 0.217 0.375 0.648

50 0.421 0.225 0.435 1.060 1.720

100 1.299 0.9 0.87 3 4.77

200 3.212 3.6 1.74 8.485 13.825

400 6.753 14.4 3.48 24 41.88

Fig. ‎6-6 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 0.4T under PWM

voltage excitation

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



178

Experimental results under PWM voltage excitation at 1.0 T 6.2.3

Increasing the peak flux density to 1.0 T, the largest measured and total power losses

were obtained as expected at 400 Hz they were 40.567 and 157.28 (W/kg)

respectively. And the smallest measured and total power losses were obtained at (25

Hz). They were 0.634 and 2.405 W/kg respectively. Table 6.2 shows total power loss

per cycle and table 6.3 summarises coefficient components of power loss when the

core was energised at 1.0 T.

Table ‎6-3 Power loss per cycle under PWM voltage excitation at 1.0 T at different magnetising

frequencies


Hz

Measured power loss

Per weight (W/kg)


(W/kg). sec

25 0.634 0.025

50 2.335 0.046

100 6.719 0.067

200 17.173 0.085

400 40.567 0.101

Table ‎6-4 Measured and total power loss component of Epstein size lamination under PWM

voltage excitation at 1.0 T with different magnetising frequencies

Frequency

(Hz)

Measured

power loss per

weight(W/kg)

Pe

(W/kg)

Ph

(W/kg)

Pa

(W/kg)

Pt =

Pa+Ph+Pa

(W/kg)

25 0.634 0.187 0.68 1.537 2.405

50 2.335 0.75 1.36 4.348 6.458

100 6.719 3 2.72 12.3 18.02

200 17.173 12 5.44 34.789 52.229

400 40.567 48 10.88 98.4 287.704

A specific power loss per cycle is plotted against the square root of frequency as

shown in Fig. 6-7. By applying the coefficients in equation 6.8 the power loss

components are automatically calculated,



179

The value of hysteresis and eddy current power loss per cycle versus magnetising

frequency is shown in Fig. 6-8.

Fig. ‎6-7 Specific power loss per cycle versus root of frequency at 1T under PWM voltage

excitation

Fig. ‎6-8 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 1T under PWM

voltage excitation

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



180

Experimental results under sinusoidal voltage excitation at 0.4T 6.2.4

Measurement of Epstein size lamination was again taken under sinusoidal flux

condition using a measurement system as shown in Fig. 6-1, and 6-2. All

measurements were taken at the same peak flux density and same magnetising

frequency as that under PWM voltage excitation. Table 6.5 shows specific power

losses per cycle and table 6.6 shows overall total losses at 0.4T as resulted under

sinusoidal excitation.

Table ‎6-5 Power loss per cycle under sinusoidal voltage excitation at 0.4 T at different

magnetising frequencies


Hz

Measured power loss per

weight (W/kg)


(W/kg). sec

25 0.073 0.0029

50 0.241 0.0048

100 0.758 0.0075

200 2.043 0.010

400 4.665 0.011

Table ‎6-6 Specific and total power loss of an Epstein size lamination under sinusoidal voltage

excitation at 0.4T and different magnetising frequencies

Frequency

(Hz)

Measured

power loss per

weight(W/kg)

Pe

(W/kg)

Ph

(W/kg)

Pa

(W/kg)

Pt =

Pa+Ph+Pa

(W/kg)

25 0.073 0.025 0.092 0.187 0.305

50 0.241 0.1 0.185 0.530 0.815

100 0.758 0.4 0.37 1.5 2.27

200 2.043 1.6 0.74 4.24 6.582

400 4.665 6.4 1.48 12 19.88

Total power loss per cycle versus square root of frequency is shown in Fig. 7-9. The

polynomial function of this curve was obtained by using the polynomial curve fitting

function in Microsoft Excel.



181

Fig. ‎6-9 Specific power loss per cycle versus square root of frequency at 0.4T under sinusoidal

voltage excitation

By applying coefficients given below those obtained from Fig. 6-9. The eddy current

power loss, hysteresis power loss and anomalous power can be calculated using

equation 6.8.

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



182

Eddy current and hysteresis power losses per cycle versus magnetising frequency at

0.4T are shown in Fig. 6-10.

Fig. ‎6-10 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 0.4T under

sinusoidal voltage excitation

6.3 Experimental results under sinusoidal voltage excitation at 1.0 T

Magnetising the core with peak flux density at 1.0 T, the largest measured and total

power losses were obtained as expected at 400 Hz they were 26.346 and 111.12

(W/kg) respectively. And the smallest measured and total power losses were

obtained at (25 Hz). They were 0.436 and 1.77 W/kg respectively. Table 6.7 shows

total power loss per cycle and table 6.8 summarise coefficient components of power

loss with the core energised at 1.0 T.

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



183

Table ‎6-7 power loss per cycle at 1.0 T at different magnetising frequencies


Hz

Measured power loss per

weight (W/kg)


(W/kg). sec

25 0.436 0.017

50 1.409 0.028

100 4.435 0.044

200 11.801 0.059

400 26.346 0.065

Table ‎6-8 Specific and total power loss of an Epstein size lamination under sinusoidal voltage

excitation at 1.0 T at different magnetising frequencies

Frequency

(Hz)

Measured power

loss per

weight(W/kg)

Pe

(W/kg)

Ph

(W/kg)

Pa

(W/kg)

Pt =

Pa+Ph+Pa

(W/kg)

25 0.436 0.125 0.545 1.1 1.77

50 1.409 0.5 1.09 3.111 4.701

100 4.435 2 2.18 8.8 12.98

200 11.801 8 4.36 24.890 37.250

400 26.346 32 8.72 70.4 111.12

Total power loss under sinusoidal voltage excitation per cycle versus square root of

frequency is shown in Fig. 6-11.



184

Fig. ‎6-11 Specific power loss per cycle versus square root of frequency at 1T under sinusoidal

voltage excitation

By applying the coefficient given below, those obtained from Fig. 6-11. The eddy

current power loss, hysteresis power loss and anomalous power loss can be

calculated using equation 6-8.

Where is the eddy current losses per cycle,

is the hysteresis

loss per cycle and is the anomalous loss per cycle. By applying equation

(6.8) the eddy current power loss, hysteresis power loss and are shown in Fig. 6-12.

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



185

Fig. ‎6-12 Eddy current and hysteresis loss per cycle versus frequency (Hz) at 1T under

sinusoidal voltage excitation

Pow

er l

oss

per

cycl

e (W

/Kg/H

z)



186


Specific and total power losses were measured under sinusoidal and PWM

excitations using Epstein size laminations. Power loss was measured at various flux

densities of 0.4T and 1.0T. Both measurements were conducted under magnetising

frequencies of 25, 50, 100, 200, and 400 Hz.

At 0.4 T measured and total power loss results variation with flux density under

PWM and sinusoidal voltage excitation are shown in tables 6.2 and 6.6. The total of

measured power loss was higher as expected under PWM waveform. Comparing the

total power loss and measured power loss under PWM waveform with the total and

measured power loss occurred under sinusoidal waveform with varied magnetising

frequency, it be seen that the total power loss results at 25 Hz magnetising frequency

under PWM waveform were found to be 52% higher than that under sinusoidal.

Increasing the magnetising frequency to 400 Hz, the loss difference between

sinusoidal and PWM voltage excitation at 400 Hz was found to be 88%, higher under

PWM voltage excitation. Furthermore, measured power loss under sinusoidal

waveform was varied between 0.073 to 4.665 W/kg, whereas measured power loss

under PWM waveform were varied between 0.098 and 6.753 W/kg.

Comparing the results obtained when Epstein frame energised at 1.0 T. as shown in

tables 6.4 and 6.8, total power loss at 25 Hz magnetising frequency was again higher

under PWM voltage excitation by 26%. And it was higher at 400 Hz magnetising

frequency under PWM voltage excitation by 61%. Furthermore, measured power

loss under PWM voltage excitation was varied between 0.634 to 40.56 W/kg and it

was varied under sinusoidal waveform between 0.436 to 26.34 W/kg.

The loss difference between PWM and sinusoidal voltage excitation was found to be

higher under PWM. Lowest loss occurred at low magnetising frequency 25 Hz and

highest loss occurred at higher magnetising frequency 400 Hz. The results of total,

measured power loss was found to be higher under PWM voltage excitation this is

due to the high harmonic distortion occurring when the Epstein size sample was

energised by PWM waveform.



187

7. CHAPTER 7

MATLAB block diagram contents 7.1.1

“MATLAB Simulink” is a powerful tool for modelling, simulating and analysing

various electrical blocks data. Therefore, the simulation of three-phase transformer

core was modelled by using the Simulink of “MATLAB 2015”. The Simulink blocks

including following:

1. Three voltage sources were used to feed the transformer with electrical power

2. Three-phase breaker used to control the braking operation

3. Three-phase voltage and current measurements were used to measure the

instantaneous DC voltage or current between two nodes

3. Three-phase transformer

4. Load switch

5. Three-phase parallel RLC load

6. Receiver signal used to receive signal from power GUI

7. Multimeter used to measure emf to calculate flux density

4. PWM Generator (2-level)

5. Universal bridge used to convert current

7. Scope used to monitor the signals

8. Bus selector used to separate signals

9. Fast Fourier Transformer FFT used to collect voltage and current harmonic

11. Power GUI block used to solve the circuit



188

These blocks are combined to produce sinusoidal signal measurement and PWM

signal measurement.

Simulation under sinusoidal voltage excitation 7.1.2

Three-phase transformer core was energised by three (AC) sinusoidal supplies. To

obtain desired flux density equation 2.16 was used to set flux density to 0.4T, 0.6T

and 1.0T respectively. And the frequency was set to 50 HZ,

Fig.7.1 and Fig. 7-2 show the overall circuit under sinusoidal excitation with load

and the overall circuit with no-load condition.

Fig. 7-1 Sinusoidal voltage excitation circuit under load condition



189

Fig. ‎7-2 Sinusoidal voltage excitation circuit under no-load condition



190

Simulation under PWM voltage excitation 7.1.3

In order to study the difference between three-phase sinusoidal voltage excitation and

three- phase PWM voltage excitation, PWM circuit was designed. Fig. 7-3 and Fig.

7-4 show the overall PWM circuit under load and no-load conditions.

Fig. ‎7-3 PWM voltage excitation circuit under load condition



191

Fig. ‎7-4 PWM voltage excitation circuit under no-load condition



192

Total harmonic distortion under sinusoidal voltage excitation 7.1.4

The harmonic content of primary current for the peak flux density of 0.4T, 0.6T and

1.0T was measured throughout the simulation under both load and no-load

conditions. The result of the harmonic analysis for the primary current can be seen in

Figs. 7-5 and Fig. 7-6. Furthermore, harmonics existing in the primary voltage under

load and no-load conditions can be seen in Fig. 7-7 and 7-8.

Fig. ‎7-5 Harmonic order content of primary current for sinusoidal supply voltage under no-load

condition with different peak flux density (T)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100 150 200 250 300 350 400 450

Per

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rm (

%)

Variation of fundamental frequency (Hz)

THD at 0.4T = 0.61%, 0.6T = 0.74% and 1.0T = 1.05%

0.4T

0.6T

1.0T



193

Fig. ‎7-6 Harmonic order content of primary current for sinusoidal supply voltage under on-load


Fig. ‎7-7 Harmonic order content of primary voltage for sinusoidal supply voltage under no-load


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

100 150 200 250 300 350 400 450

Per

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rm (

%)


THD at 0.4T = 1.65%, at 0.6T = 2.36% and 1.0T = 3.08% 0.4T

0.6T

1.0T

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

100 150 200 250 300 350 400 450

per

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rmer

(%

)


THD at 0.4T =0.51, 0.6T= 0.70 and 1.0T = 0.98% 0.4T

0.6T

1.0T



194

Fig. ‎7-8 Harmonic order content of primary voltage for sinusoidal supply voltage under on-load


7.2 Total Harmonic Distortion, THD under PWM Voltage Excitation

THD of primary current and primary voltage was computed throughout the

simulation under both load and no-load conditions. Fig 7-9 and 7-10 show THD of

the primary current under load and no-load conditions, and Fig 7-11 and 7-12 shows

THD in secondary voltage under load and no-load conditions with different peak flux

density under load condition.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

100 150 200 250 300 350 400 450

per

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rm (

%)


THD at 0.4T = 0.59, 0.6T = 1.48% and 1.0T = 2.20%

0.4T

0.6T

1.0T

Hz



195

Fig. ‎7-9 Harmonic order content of primary current for PWM supply voltage under on-load


Fig. ‎7-10 Harmonic order content of primary current for PWM supply voltage under no-load


0

2

4

6

8

10

12

14

16

18

20

100 150 200 250 300 350 400 450

Pe

rce

nta

ge o

f th

e f

un

dam

en

tal w

ave

form

(%

)


THD at 0.4T = 4.73%, 0.6T = 5.88% and 1.0T = 7.29% 0.4T

0.6T

1.0T

0

2

4

6

8

10

12

100 150 200 250 300 350 400 450

Per

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rm (

%)


THD at 0.4T = 3.54%, 0.6T = 3.55% and 1.0T = 5.97%

0.4T

0.6T

1.0T



196

Fig. ‎7-11 Harmonic order content of secondary voltage for PWM supply voltage under on-load


Fig. ‎7-12 Harmonic order content of secondary voltage for PWM supply voltage under no-load


0

2

4

6

8

10

12

14

100 150 200 250 300 350 400 450

Per

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rm (

%)


THD at 0.4T= 7.05%, 0.6T = 8.14% and 1.0T = 10.43%

0.4T

0.6T

1.0T

0

2

4

6

8

10

12

14

16

100 150 200 250 300 350 400 450

pre

cen

tag

e o

f th

e fu

nd

am

enta

l w

av

efo

rm (

%)


THD at 0.4T= 6.68%, 0.6T = 6.09% and 1.0T = 6.40% 0.4T

0.6T

1.0T



197

Total harmonic contents with a change in switching frequency 7.2.1

Fig. 7-12, 7-13, 7.14 and 7.15 below show how total harmonics of primary and

secondary current and voltage are affected by switching frequency.


condition at switching frequency 3 kHz



0

2

4

6

8

10

12

14

16

18

20

100 150 200 250 300 350 400 450


THD at 0.4T= 3.22%, 0.6T= 5.53 %and 1.0T= 6.78%

0.4T

0.6T

1.0T

0

2

4

6

8

10

12

14

100 150 200 250 300 350 400 450


THD at 0.4T= 6.21%, 0.6T= 6.37% and 1.0T= 6.76% 0.4T

0.6T

1.0T



198





0

2

4

6

8

10

12

14

16

18

100 150 200 250 300 350 400


THD at 0.4T= 2.72%, 0.6T= 5.17% and 1.0T 6.22% 0.4T

0.6T

1.0T

0

2

4

6

8

10

12

100 150 200 250 300 350 400 450


THD at 0.4T=5.13%, 0.6T= 5.19% and 1.0T= 5.73% 0.4T

0.6T

1.0T



199

Harmonic analysis 7.2.2

Fig. 7-5 to Fig. 7-8 show that the sinusoidal supply has an insignificant amount of

harmonic present. The most predominant harmonic of the primary and secondary

currents and voltage under load and no-load condition is the 5th

. This harmonic

becomes more distorted on the output of the core when the core operated under load

condition compared to the others when the core operated under no-load condition.

Fig. 7-9 to Fig. 7-12 shows that the most predominant harmonic distortion caused by

PWM waveform is the 5th

. It is clearly shown that there is a higher harmonic content

under PWM waveform compared to the sinusoidal excitation. This may suggest that

PWM will create higher harmonic contents in the core producing higher losses

compared to a sinusoidal input.

The odd harmonic rises proportionally with the peak flux density within the core

under sinusoidal and PWM excitation, therefore the harmonic content is a factor

leading to the increase in losses. A comparison of the Figs. 7-5, 7-6, 7-7, and 7-8

illustrates that little distortion occurs in the core when the core is excited by a

sinusoidal input, the main distortion harmonics are in 3rd

and 5th

. The slight

harmonics distortion may account for some of the losses incurred by the sinusoidal

excitation.

From Fig. 7.13 to Fig. 7.16 show the PWM primary current waveform shows slightly

lower magnitude on all harmonic components across the whole range of different

peak flux densities compared to the secondary voltage. And also it can be observed

that the amplitude of total harmonic component at low switching frequency were

higher than that at a high switching frequency. For example the reduction in total

harmonic distortion in the primary current Fig. 7-13 and Fig. 7-15 at 0.4T, 0.6T and

1.0T were 15%, 6.5% and 8.2% respectively lower at higher switching frequency of

5 kHz.

Comparing the effect of switching frequency on total harmonic distortion occurred in

the secondary voltage Fig. 7-14 and Fig. 7-16 it can obtained that at 0.4T, 0.6T and

1.0T the reduction in total harmonic components were 17%, 18% and 15%

respectively lower at higher switching frequency, this was due to the reduction of



200

Amplitude of harmonic components and reduction of harmonic contents in the core

flux density waveform with increased switching frequency. These results confirmed

the validity of the analysis carried out at other measurements. It was found the power

loss and vibration of the core was decreased with increase in switching frequency. So

these results present the benefit on the performance of the transformer core at high

switching frequency.

Power loss analysis 7.2.3

Transformer loss can be categorized into two major groups no-load and load loss.

The losses measured under no-load conditions in transformers consist of hysteresis

and eddy current losses in core laminations and it is manifested as the heat generated

in the core for example, when there is no current flowing in the secondary coil then

transformer said to be on no-load. Even when the transformer is on no-load, current

known as the exciting current flows in the primary winding because of the core

losses and the finite permeability of any practical transformer core. The exciting

current can be considered as having two components, the core losses current and the

magnetising current. The no-load core loss was measured by using a “Scope”

through multiplying the primary phase currents, , and by the primary phase

voltage, , and . Dividing the component losses by the weight of the

transformer core gives the value of power loss/weight.

On the other hand, when the transformer is operated under load condition, the no-

load core loss per weight can be calculated through multiplying the three-phase

primary currents , and by the three-phase secondary voltage and and

then dividing and then divides the product by the weight of the transformer core.

Fig.7-19. Shows the change in total losses of the transformer core with a change in

peak flux density under sinusoidal and PWM voltage excitations under no load

conditions.



201

Fig. ‎7-17 Overall power loss of three-phase transformer core supplied by sinusoidal and PWM

waveforms with change in the peak flux density (T) at 50 Hz at Mi= 0.5 and Fs= 3kHz

From Fig. 7-19 result shows that total power losses produced by various excitations.

And increased under all excitations as the peak flux density increases, nevertheless

all the excitation displays more increase in losses when the core was excited under

load condition, for example. At the peak flux density of 1.0T the difference in

losses with each excitation becomes most apparent. The sinusoidal excitation

demonstrates the lowest increase losses through the whole range of peak flux

densities, but this excitation still suffers from 54 W/kg rise in losses from 0.4T to

1.0T. However, under no-load condition power losses suffers from 38W/kg. All

PWM modes tested show higher total losses compared to sinusoidal excitation. The

most significant increase in losses from those graphs occurred when the PWM

inverter was set with low modulation index and low switching frequency.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

No-load Load No-load Load

Sin Sin PWM PWM

Ov

era

ll p

ow

er l

oss

(W

/kg

)

0.4T

0.6T

1.0T



202

Specific losses with a change in PWM modulation index 7.2.4

Fig. 7-20 Shows how the total power losses of the core change with change in the

modulation index at varying core flux density at = 3 kHz. Fig. 7-21 Shows how

change in modulation index affects the total power losses of the core at = 2 kHz.

Fig. 7-22 shows how a change in modulation index affects the total power loss of the

core at = 1 kHz.

Fig. ‎7-18 Total power losses of the three-phase transformer core supplied by PWM waveform

with change in the modulation index at 3kHz switching frequency.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

T

ota

l p

ow

er l

oss

(W

/kg

)

0.4T

0.6T

1.0T

PWM

Mi=0.6

𝑓𝑠=3kHz

PWM

Mi=0.7

𝑓s=3kHz

PWM

Mi=0.8

𝑓𝑠=3kHz

PWM

Mi=1.0

𝑓𝑠=3kHz

PWM

Mi=0.5

𝑓𝑠=3kHz



203


with change in the modulation index at 2kHz switching frequency


with change in the modulation index at 1 kHz switching frequency

0

0.2

0.4

0.6

0.8

1

1.2

1.4

To

tal

po

wer

lo

ss (

W/k

g)

0.4T

0.6T

1.0T

PWM

Mi=0.6

𝑓𝑠=2kHz

PWM

Mi=0.7

𝑓𝑠=2kHz

PWM

Mi=0.8

𝑓𝑠=2kHz

PWM

Mi=1.0

𝑓𝑠=2kHz

PWM

Mi=0.5

𝑓𝑠=2kHz

1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

To

tal

po

wer

lo

ss (

W/k

g)

PWM

Mi=0.5

𝑓𝑠=1 kHz

0.4T

0.6T

1.0T

PWM Mi=0.6 =1 kHz

PWM

Mi=0.7

=1 kHz

PWM

Mi=0.8

=1 kHz

PWM Mi=1.0 =1 kHz



204

Fig. 7-20 to Fig 7-22 demonstrate that the total power loss increases with peak flux

density. It also illustrates that as the modulation index of the PWM input waveform

increases the losses from the core decrease. The highest total power losses when the

modulation index is equalled to 0.5, the difference in losses as the modulation index

increases becomes less apparent as the core peak flux density was reduced and it

could conclude that even at the lower switching frequency of 1 and 2 kHz an increase

in excitation modulation index gives rise to a decrease in the core losses.

Total losses with a change in PWM switching frequency 7.2.5

This assortment of graphs show how switching frequency affects the total power loss

at various modulation index and peak flux densities at 50Hz fundamental. The graphs

showing the effects of switching frequency with changing of modulation index of

0.5, 0.7, and 1.0 can be seen in Fig. 7-23 to Fig 7-24.

Fig. ‎7-21 Total power loss of the three-phase transformer core with change in switching

frequency at constant modulation index of 0.5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.4T 0.6T 1.0T

To

tal

po

wer

lo

sses

(W

/kg

)

Peak flux densities (T)

3kHz

2kHz

1kHz



205





0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.4T 0.6T 1.0T

To

tal

po

wer

lo

ss (

W/k

g)

Peak flux densities

3kHz

2kHz

1kHz

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.4T 0.6T 1.0T

To

tal

po

wer

lo

ss (

W/k

g)

Peak flux densities

3kHz

2kHz

1kHz



206

From Fig. 7-23 to Fig. 7-25, the effect of the switching frequency was compared.

These graphs show that as the switching frequency is increased the losses of the core

are reduced. At the peak flux density of 1.0T, = 1 kHz, the loss is 1.20 W/kg this

is then reduced by 22% when the switching frequency increased to 2 kHz. Further

reduction in losses can be seen when the switching frequency is increased from 2

kHz to 3 kHz. When the flux density is reduced, the losses of the core decrease this

could demonstrates that the effect of changing the switching frequency on the core

losses is reduced when the peak flux density is reduced. Furthermore, figures exhibit

that the core losses with changing switching frequency. The losses are reduced as

switching frequency is increased.

By comparing all the graphs, it can be seen that by increasing the switching

frequency the losses of the core are decreased. The effect of increasing switching

frequency to reduce the core losses, the greatest difference in losses between the

sinusoidal excitation and PWM excitation occurs when the lowest switching

frequency is applied. The highest switching frequency for a PWM excitation exhibits

the least difference in losses compared to the sinusoidal excitation.

Summary 7.2.6

It was found that the modulation index contributed to the largest variation in total

power loss caused by PWM excitation. This distorted voltage condition led the three-

phase transformer losses of 1.53 W/kg fig 7.22 at the lowest modulation index of 0.5

and a switching frequency of 1 kHz. This occurred when the core was saturated at a

peak flux density of 1.0T.

When the modulation index was increased to 1.0 at switching frequency of 3 kHz fig.

7.20 these losses are reduced to 7%. The experimentation shows that as the switching

frequency increased from 1 kHz to 3 kHz, the losses decreased.

This chapter has shown that application using transformer excited by PWM inverter

can be improved to reduce total power losses, it appears selecting a PWM setting

with a modulation index of 1.0 at switching frequency 3 kHz is given the best results.



207

CHAPTER 8

8. Conclusion and suggestion for future work

Conclusion 8.1.1

In this thesis, magnetic properties of the electrical steel laminations such as flux

density distribution, localised and overall power losses, and localised

magnetostriction distribution were studied over a wide range of magnetisation. The

investigations have shown that these properties strongly depend on the material

properties, especially at high frequencies, where localised magnetostriction and flux

density along the laminations of the transformer core is distributed almost uniformly.

Increasing the magnetising frequency leads to the distribution of the flux density to

be non-uniform which increases the core noise. Further, the results showed that the

distribution pattern of flux density and localised magnetostriction has strong

dependence on the magnetising frequency and relative permeability of the material.

Further observations from this investigation are as follows:

1. PWM causes power loss to increase in electrical steels compared to sinusoidal

excitation due to the increase in both magnetostriction and vibration of the core. The

ratio of loss increase is dependent on operating flux density, and PWM voltage

excitation parameters. For example losses of three-phase transformer increased under

low switching frequency and low modulation index.

2. Preliminary measurements of against frequency seem to show that hysteresis

and eddy current components of loss changes under PWM excitation. The reason for

this is expected to be related to the very rapid domain switching which occurs at

certain times in the PWM excitation cycle. The variation of specific power losses

under PWM flux waveform with different peak flux densities show quadratic relation

same as those under sinusoidal excitation.

3. It has been shown that increasing the magnetic flux density causes an increase in

power loss and in strain of the core due to the increase in magnetostriction.



208

4. The result from this investigation suggests that transformer energised by PWM

inverter can be improved by selecting a PWM setting with high modulation and high

switching frequency which will lead to reduction in power loss.

5. Localised magnetostriction is more significant when a core is operated at high

flux density due to increased air gap in the joints.

6. When the core energised under PWM voltage excitation at low flux density, higher

core strain is generated from in-plan direction of the lamination on its side surface

than from the front and the top surface. However, at high flux density, higher strain

is generated from the out of plan direction of the laminations due to an increase of

both magnetostriction and magnetic force.

7. The highest strain levels were obtained at the joint and corner areas due to the out

of the rolling direction magnetisation that results in high rolling direction of

magnetostriction.

8. This research demonstrated that when a transformer core is operated at low 0.4T

and 0.6T then higher core noise is generated from in-plan direction of the lamination

on it is side surface than from the front and the top surface. Whereas, at high flux

density of 1T, higher noise is generated from the out-of-plan direction of the

laminations due to an increase of both magetostriction and magnetic force.



209

Suggestion for future work 8.1.2

The present investigation has given rise to a number of specific areas worthy of

future investigation.

1. Further comparison of magnetostriction measurement system would be very useful

in order to develop recognised methods to measure mgnetostriction. For example,

measurement of magnetostriction in the form of Epstein strips under PWM voltage

excitation with stress should be carried out. After analysing measurement results,

would be good to investigate the PWM parameters, for example modulation index

and switching frequency effects on magnetostriction under stress condition.

2. A future study may consider ways in which to reduce the power losses created at

higher flux density.

3. Verifying magnetic process under PWM voltage excitation by magnetic domain

observation in order to optimise the performance of the transformer core under such

complex waveform could be beneficial.

4. Investigation on how magnetic circuit geometries affect power loss under PWM

voltage excitation could be considered.

5. Additional study of the core flux distribution is needed to look into the exact effect

of the core strain distribution.

6. Geometry-dependent magnetostriction should be investigated because the

demagnetisation factor affects magnetostriction, which may cause high errors in

calculation of deformation and vibration in transformer core.

7. The performance of magnetostriction and power losses has been investigated on a

bare model transformer core operating under PWM voltage excitation. Therefore, if



210

practically possible future research should continue to determine the influence of

windings, oil and tanks etc.

8. Multi- physics model simulating the magnetostriction distribution and magnetic

flux density distribution is necessary in order to estimate the effect of

magnetostriction on the flux waveform. If the material characteristics are known then

specific losses can be estimated from the flux waveforms.



211

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